CN112862144B - Method for determining optimal loss curve of non-data city based on double-layer target optimization - Google Patents
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Abstract
The invention discloses a method for determining an optimal loss curve of a double-layer target optimized non-data city based on a variation coefficient and beta distribution optimization principle, which is used for reducing uncertainty in a data processing process. Firstly, transferring loss rate values of a data reference area to a research area aiming at inland plain cities of disaster-lack data by referring to a comparison principle; and secondly, based on a preferred principle that the variation coefficient is minimum and the beta distribution probability is maximum, reducing the quotation error and the statistical error generated in the loss rate quotation, acquiring a relatively accurate investigation region loss value, and further establishing a disaster-suffering water depth-loss rate relation curve of the disaster-lack data city. Therefore, the generalized non-data city disaster damage curve fitting method taking the regional index value as an input parameter and the damage curve as an output result is formed, and scientific reference is provided for the establishment of a non-data city flood damage curve.
Description
Technical Field
The invention relates to the technical field of flood damage assessment, in particular to a method for determining an optimal damage curve based on a double-layer target optimization non-data city.
Background
In the world extreme weather event frequency and urban setting, the frequency and severity of urban flood disasters is increasing dramatically. Accurately and reliably quantifying flood losses is necessary to implement effective urban flood risk management. Urban flood loss assessment depends on flood characteristics, economic and geographical conditions of flood-prone areas and the like, and has the characteristics of multidimensional, differential and multidisciplinary comprehensive integration. The most common flood loss assessment method is to connect flood flooding depths with disaster loss curves (depth damage functions), building types and economic factors to form loss results, which are considered as internationally accepted standard methods for quantitatively assessing urban flood losses. Therefore, the formation of a scientific generalized damage curve construction method is critical to the quantification of damage.
Typically, the main sources of urban damage curves are fitted based on government statistical or researcher-investigated damage data, and these empirical damage curves constructed based on typical case data are the current main research and development modes. And secondly, experience loss curves developed by the management of the whole country or region, which are usually established on the basis of a large amount of investigation data. However, empirical flood loss curves are applicable to the original data coverage space, but such spatially dependent local loss curves do not perform well in space transfer. In different flood event and process types, factors affecting building loss have spatio-temporal heterogeneity, which results in low effect of local models in migration settings.
However, most cities worldwide lack or even have no complete and accurate historical disaster damage data. The conventional approach of fitting a spatial dependent empirical loss curve with the loss data for a particular flood event is difficult for most non-informative cities. To solve this problem, a few studies have been directed to using the typical loss curve of a similar city. In flood vulnerability analysis, uncertainty is unavoidable due to the spatial variability of the risk components, but the damage model transferred from direct other areas more expands uncertainty of the loss results. Or a proportional relation is established between a certain city and an index, and the loss curve is corrected to achieve the purpose of use. These studies provide a viable idea for the construction of loss curves in non-informative regions, but they do not consider the problem of uncertainty in the loss rate results due to the contingency of setting a single city and index as comparison objects.
Due to the limitation of regional history data, it is difficult to develop a generalized flood loss curve construction method suitable for a non-data region. However, with the high-speed development of the global urbanization process, due to the unbalanced development of the disaster-bearing environment and disaster prevention capability of the city, property loss caused by flooding cannot be ignored, and the establishment of a flood loss curve evaluation method aiming at different non-data areas is urgent to support the management of urban flood risks.
From the analysis of the current situation of research, borrowing effective data from a plurality of areas and eliminating uncertainty is the most effective method at present. In addition, a large number of flood loss curves are accumulated in frequent flood cities under the background of big data at present, and a data mining foundation is laid for the invention. However, how to eliminate uncertainty in space transfer of other urban loss curves is a challenge to be solved.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the defects of the prior art and providing a method for determining an optimal loss curve of a non-data city based on double-layer target optimization of a variation coefficient and beta distribution optimization principle, wherein uncertainty in loss rate space transfer is reduced through double-layer target optimization on the basis of sample data expansion.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for determining an optimal loss curve based on a double-layer target optimized non-material city comprises the following steps:
s1: for research cities, m reference cities are selected, and loss rate moment composed of the m reference cities is constructedArray R 0 ：
S2: k characteristic indexes are selected, and n different combination schemes are formed through the K characteristic indexes:
in the formula (3), the amino acid sequence of the compound,representing the number of schemes for K characteristic indexes to select K index combinations;
s3: feature integrated values of the study city and the reference city under n combination schemes are calculated respectively:
ream CI j Representing the feature integrated value of the research city under the j scheme, j=1 to n; order theRepresenting the feature integrated value of the ith reference city under the jth scheme, i=1 to m; wherein, the index value of the single index scheme is the integrated value; the multi-index scheme is converted into a comprehensive value through index weight;
s4: let lambda set ij Is the ith th Reference city j th Transfer coefficient of scheme, letObtaining a transfer coefficient matrix A of m multiplied by n combination schemes:
s5: based on the above, a m×n order study city loss rate matrix R is calculated:
s6: obtaining an optimal characteristic scheme based on a minimum optimization principle of a variation coefficient by using a loss rate matrix R
S7: according to the best modeThe following column vector is fitted with a beta distribution curve, and the maximum probability corresponding value of the curve is extracted as the optimal loss rate R;
s8: and repeating the steps S1 to S7, and calculating the optimal loss value of each property type under each water depth level, so as to obtain a water depth-loss rate relation curve of each property type.
Further, in the step S3, for the jth multi-index scheme including S indexes, j=k+1 to n, a projection pursuit model based on chaotic particle swarm optimization is adopted to calculate the weight, and a specific calculation flow is as follows:
s3-1: the ith index value I for the ith city is I=1 to m+1, s=1 to S, and I is calculated is Standard value of (2)
Wherein, the formula (6) is used for processing the larger and more optimal type index, and the formula (7) is used for processing the smaller and more optimal type index;
s3-2: calculating the projection integrated value CI of the ith city under the jth scheme by the formula (8) ij ：
In the formula (8), i=1 to m+1, j=k+1 to n, W S Projection weights which can be optimized for the index;
s3-3: calculating a projection objective function Q (W) by the method (9) S ) And the constraint is set as close to 1 as possible by equation (10):
maxQ(W S )＝S D |R| (9)
here, S D For projection integrated value CI ij Standard deviation of (2); r is projection integrated value CI ij Correlation coefficient with experience level.
Further, in the step S6: optimal characteristic scheme based on principle of minimal optimization of variation coefficientThe specific flow of (a) is as follows:
s6-1: calculating a variation coefficient CV of each column vector of the loss rate matrix R from the formula (13) j And the variation coefficient set CV is formed by the formula (14):
CV＝[CV 1 ,CV 2 ...CV j ...CV n ] T (14)
wherein ,uj Mean value of j-th group column vector, sigma j Variance for the j-th set of column vectors;
s6-2: extracting a column vector with the smallest variation coefficient from the formula (15), wherein the corresponding s-th scheme is the optimal scheme
Further, the specific flow in the step S7 is as follows:
s7-1: according to the distance estimation methodThe value of the m sample loss in the water depth is subjected to beta distribution parameter estimation, and the beta distribution overall average E (R) under the water depth is calculated by the formula (18) and the formula (19) respectively ij ) Sum variance Var (R) ij )：
Wherein μ and σ are the mean and variance of the sample loss rate, respectively;
alpha and beta are calculated from the following formula:
wherein ,for the distance estimation of the loss curve alpha +.>Distance estimator for β;
s7-2: and determining a beta distribution curve according to the distance estimation parameters alpha and beta, and extracting a maximum probability corresponding value as an optimal loss rate R.
The beneficial effects of adopting above-mentioned technical scheme to produce lie in:
flood loss assessment research is an important part of urban flood risk management, and the establishment of a disaster damage curve is more key to loss assessment research. Fitting a loss curve through historical data for a non-informative city is difficult due to data constraints. Spatial transfer of inter-region loss curves is generally an effective method, but suffers from data referencing and statistical uncertainty. Therefore, the invention provides a method for determining an optimal loss curve of a double-layer target optimized non-data city based on a variation coefficient and beta distribution optimization principle, so as to reduce uncertainty in a data processing process. Double-layer data capacity expansion is carried out by referring to the object data layer and the characteristic index data layer, traditional single selectable data are changed into selectable data matrixes, and then the optimal loss rate value is obtained based on double-layer optimization with minimum variation coefficient and maximum probability.
1. The invention constructs the research area loss rate matrix through large sample data and selects the characteristic scheme set with the minimum discrete degree to reduce the uncertainty in the data reference process.
2. According to the invention, the regional experience parameter is used for restraining the loss rate beta distribution in the traditional research through sample data capacity expansion, so that the heterogeneity of regional parameters is realized.
3. The invention forms a probability model of the loss rate and provides a quantification of each loss rate probability value. And combining the probability of flood disasters, establishing joint distribution to quantitatively calculate the occurrence size and probability value of the final loss result. This provides some technical support for pre-disaster prevention and expected loss.
Drawings
FIG. 1 is a frame diagram of a method for determining a flood loss curve of a non-material city;
FIG. 2 is a schematic diagram of extracting loss rate probability maxima based on beta distribution;
FIG. 3 is a diagram showing an example of a preferred set of patterns under a commercial-interior property-4 level water depth (where, plot a is 0.5m, plot b is 1.5m, plot c is 2.5m, and plot d is 3.5 m);
FIG. 4 is a graph of the maximum probability loss rate value results for all depths of water for a business-house;
FIG. 5 is a graph comparing business-house all water depth optima and protocol sets;
FIG. 6 is a graph of loss rates for all property types;
FIG. 7 is a statistical graph of the optimal solution loss rate set for 10 loss curves and the variation coefficient of the raw data;
fig. 8 is an optimal value and average probability comparison for 10 property types (upper curve represents probability of optimal value +3 sigma interval, lower black represents probability of average value +3 sigma interval, sigma is variance of scheme set, fig. a is industry-house, fig. b is industry-equipment, fig. c is industry-inventory, fig. d is road, fig. e is business-business, fig. f is business-interior property, fig. g is house-house, fig. h is house-interior property, fig. i is public service-service, and fig. j is public service-interior property).
Detailed Description
The invention will be described in further detail with reference to the drawings and the detailed description.
Flood loss curves are one of the most common methods of flood loss estimation worldwide. Loss rate is defined as the ratio of potential damage value to the total amount of risk assets at a certain depth of inundation. The loss curve is a curve composed of defined multi-level loss rate data points at water depths.
In the present invention, a non-data city is also called a research area or a research city, and a data city is also called a reference area or a reference city.
In a non-data city, the flood disaster loss rate is obtained by a hydrologic comparison method, namely the loss rate (R 0 ) The investigation region loss rate (R) is deduced, and the quoted region loss rate is converted into the investigation region loss rate through the characteristic index (I) affecting disaster loss, and the conversion process is shown in the formula (1).
But current research only considers a single reference city as a comparison object. Secondly, the selected indexes are too single, only focus on the urban economic level, and neglect the influence of other factors, such as disaster-bearing environment and disaster prevention and reduction capability. The low representativeness and contingency of a single comparison object leads to an increase in uncertainty in the loss rate determination process.
As shown in FIG. 1, the invention discloses a method for determining an optimal loss curve based on a double-layer target optimized non-material city, which comprises the following steps S1-S7.
Firstly, in order to reduce uncertainty in loss rate space transfer, the method expands the number of quoted cities, expands the number of quoted cities into various schemes through multi-index combination, and expands a single loss rate result into an optional loss rate matrix R according to a formula (1), wherein the steps are as S1-S5.
Next, the invention establishes a research target by setting a double-layer optimization principle: and calculating the optimal loss rate R under each stage of water depth from the loss rate matrix R. And in the continuous optimizing process, the reference and the statistical uncertainty of the loss rate space transfer result of the non-data area are reduced, and the method is divided into two steps S6-S7.
S1: for research cities, m reference cities are selected, namelyConstructing a loss rate matrix R consisting of m referenced cities 0 ：
S2: k characteristic indexes are selected, and n different combination schemes are formed through the K characteristic indexes:
in the formula (3), the amino acid sequence of the compound,representing K number ofThe characteristic index selects the scheme number of k index combinations;
s3: feature integrated values of the study city and the reference city under n combination schemes are calculated respectively:
ream CI j Representing the feature integrated value of the research city under the j scheme, j=1 to n; order theRepresenting the feature integrated value of the ith reference city under the jth scheme, i=1 to m; wherein, the index value of the single index scheme (j=1 to K) is the integrated value; the multi-index scheme (j=K+1-n) is converted into a comprehensive value through index weight, and the weight is calculated by adopting a projection pursuit model (PP-CPSO) based on chaotic particle swarm optimization;
s4: let lambda set ij Is the ith th Reference city j th Transfer coefficient of scheme, letObtaining a transfer coefficient matrix A of m multiplied by n combination schemes:
s5: based on the above, a m×n order study city loss rate matrix R is calculated:
s6: obtaining the optimal characteristic scheme based on the principle of minimal optimization of the variation coefficient, namely calculating the variation coefficient of each column vector (the loss rate set corresponding to each scheme) in the loss rate matrix R, and selecting the minimal value from the variation coefficients, wherein the corresponding scheme is the optimal scheme
S7: according to the best modeThe following vector is fitted with a beta distribution curve, and the maximum probability corresponding value of the curve is extracted as the optimal loss rate R, so as to reduce the uncertainty of the loss rate set data statistics.
S8: and repeating the steps S1 to S7, calculating the optimal loss value of each property type under each water depth level, and further obtaining a water depth-loss rate relation curve of each property type.
In the step S3, the projection tracking model (PP) is sufficiently concentrated due to the low-dimensional space data points when the high-dimensional data is reduced, and the disturbance of the irrelevant variables is avoided. For the j-th multi-index scheme containing S indexes, j=K+1-n, a projection pursuit model (PP-CPSO) based on chaotic particle swarm optimization is adopted to calculate the weight, and the specific calculation flow is as follows:
s3-1: the ith index value I for the ith city is The city here includes a study city and m reference cities, i=1 to m+1, s=1 to S, and I is calculated is Standard value of (2)
Wherein, the formula (6) is used for processing the larger and more optimal type index, and the formula (7) is used for processing the smaller and more optimal type index;
s3-2: calculating the projection integrated value CI of the ith city under the jth scheme by the formula (8) ij ：
To S dimensionConverted to be of optimal weight W S One-dimensional projection integrated value CI for projection direction ij ；
In the formula (8), i=1 to m+1, j=k+1 to n, W S Projection weights which can be optimized for the index;
s3-3: to obtain the structural features of the multi-dimensional array, the projection complex value CI ij Consideration is neededIs a data feature of (a). Thus, CI ij Standard deviation S of (2) D and CIij The absolute value of the correlation coefficient r with the empirical evaluation level should be the maximum possible. Calculating a projection objective function Q (W) by the method (9) S ) And the constraint is set as close to 1 as possible by the expression (10). The solution of the projection objective function is a complex nonlinear optimization problem, and the invention aims to solve the problem by adopting a chaotic particle swarm optimization algorithm (CPSO).
maxQ(W S )＝S D |r| (9)
Here, S D For projection integrated value CI ij Standard deviation of (2); r is the projection integrated value CI ij Correlation coefficient with experience level.
Searching for optimal solution by setting multiple characteristic solutionsTo reduce uncertainty in employing multiple reference cities and metrics. At the same flood depth, the loss rate curves should exhibit a relatively consistent or very similar trend, although the regional losses at different economic levels are very different. Therefore, the loss rate sets after urban conversion are referenced differently under the same scheme, and the degree of dispersion should be as low as possible. The Coefficient of Variation (CV) is a good characteristic of data separationThe degree of dispersion. Therefore, the invention constructs the principle of minimal optimization of the variation coefficient and extracts the optimal characteristic scheme.
In the step S6, the optimal feature scheme is obtained based on the principle of minimum optimization of the variance coefficientThe specific flow of (a) is as follows:
s6-1: the loss rate set for each feature scheme corresponds to the column vector values of the loss rate matrix R. Calculating a variation coefficient CV of each column vector of the loss rate matrix R from the formula (13) j And the variation coefficient set CV is formed by the formula (14):
CV＝[CV 1 ,CV 2 ...CV j ...CV n ] T (14)
wherein ,uj For the average value of the j-th group of column vectors, u j ＝(R 1j +R 2j …R mj )/n；σ j For the variance of the j-th set of column vectors,
s6-2: extracting a column vector with the smallest variation coefficient from the formula (15), wherein the corresponding s-th scheme is the optimal scheme
Optimal scheme under each level of water depth obtained by the formula (9)There are m converted loss rate sets. To reduce uncertainty in the statistics of the loss rate set data, the method uses optimizationThe scheme set fits probability distribution, and the maximum value R of probability is selected as the optimal result. The beta distribution is chosen such that the damage score is greater than or equal to zero and less than or equal to unity, and the beta distribution interval may also be concentrated on a small probability in view of the statistical uncertainty of the loss curve.
The probability density function of the β distribution is defined as follows:
where α and β are the shape parameters of the β distribution, α >0, β >0.
The probability maximum optimization flow in the step S7 is as follows:
s7-1: according to the distance estimation methodThe value of the m sample loss in the water depth is subjected to beta distribution parameter estimation, and the beta distribution overall average E (R) under the water depth is calculated by the formula (18) and the formula (19) respectively ij ) Sum variance Var (R) ij )：
Wherein μ and σ are the mean and variance of the sample loss rate, respectively;
alpha and beta are calculated from the following formula:
here the number of the elements is the number,for the distance estimation of the loss curve alpha +.>Distance estimator for β;
s7-2: and determining a beta distribution curve according to the distance estimation parameters alpha and beta, and extracting a maximum probability corresponding value as an optimal loss rate R, as shown in fig. 2.
In order to more accurately estimate the loss rate value of a research area (research city), the invention adopts large sample data, considers the reference area (research city) as much as possible, and changes the characteristic index from a single index into a comprehensive scheme set which considers different characteristic index combinations. Thus, the single loss rate selectable by the investigation region is extended to a loss rate transfer matrix. The uncertainty is reduced through a double-layer target principle, and the optimal loss rate value under each level of water depth is selected. The method comprises the following specific steps: firstly, transferring loss rate values of a data reference area to a research area aiming at inland plain cities of disaster-lack data by referring to a comparison principle; and secondly, based on a preferred principle that the variation coefficient is minimum and the beta distribution probability is maximum, reducing the quotation error and the statistical error generated in the loss rate quotation, acquiring a relatively accurate investigation region loss value, and further establishing a disaster-suffering water depth-loss rate relation curve of the disaster-lack data city. Therefore, the generalized non-data city disaster damage curve fitting method taking the regional index value as an input parameter and the damage curve as an output result is formed, and scientific reference is provided for the establishment of a non-data city flood damage curve.
The loss curves of 10 property types were calculated and the results analyzed in the non-data area-Zhengzhou city of China as a study area. Compared with the original data, the average variation coefficient of the optimal scheme set is reduced by 0.1; compared with the average value, the optimal value probability is comprehensively improved by 1.39 percent.
Model input (one)
The characteristic index and the reference city loss curve are key input factors of the matrix according to the composition of the loss rate matrix R. And the classification of urban land types is a precondition for the classification calculation of the loss curve. Therefore, the characteristic index, the reference city and the land type are input as models, and the building process is as follows.
(a1) Urban land type division
In order to highlight the complex characteristics of urban land utilization and improve the accuracy of loss accounting, land types are divided into 8 types based on the combination of network longitudinal source data (such as Google map) extraction and artificial visual interpretation, and the types are respectively industry, business, residence, public service, road, water body, green land and bare land. And the calculated construction sites are divided into 10 property types as shown in table 1. The water depth-loss rate relationship for each property type was calculated in turn and the water depth was divided into 40 levels (0.1-4.0 m).
TABLE 1 urban construction land type and property type dividing table
(a2) Collection of reference loss rate curves
Under the background of big data, taking China cities as search ranges, collecting urban flood loss curves appearing in all researches, and obtaining 12 data materials capable of referring to cities: jinan, puyang, harbin, zhuhai, shenyang, changchun, guangzhou, shanghai, wuxi, wenzhou, tianjin, shenzhen, i.e. m=12.
(a3) Establishment of characteristic index
In the selection of the index, people use a person-average GDP, and people use person-average deposit (PCDI) and a region total production value (GRDP), thereby indicating that the characteristic index is not fixed. However, only economic level indexes are considered in the traditional research, and the influence of disaster-bearing and disaster-preventing factors on the flood loss rate is ignored. And the disaster damage rate is the ratio of the flood damage value to the pre-disaster value, the latter is mainly influenced by the economic level, but the former is often the result of the comprehensive action of various disaster-bearing factors. Therefore, the invention considers disaster prevention capability and disaster-bearing environmental characteristics, such as urban river network density, urban pipe network density and water permeable area ratio (greening rate), on the basis of selecting economic level indexes. The characteristic index system is shown in Table 2. The characteristic schemes formed by the method are 31 in total, wherein 5 single-index schemes, 10 double-index schemes, 10 three-index schemes, 5 four-index schemes and 1 five-index scheme are adopted.
TABLE 2 characteristic index System for influencing flood loss Rate
(II) results and analysis
(b1) Selection of optimal loss rate set
The results of the business-interior property-water depths of 0.5m, 1.5m, 2.5m, 3.5m preference sets are shown in fig. 3. The set of schemes selected at 4 depths was different, A3, a24 and a234 respectively, with corresponding variation coefficients 0.4301, 0.2631, 0.2075 and 0.3154 respectively. It can be seen that some scheme sets have obvious discrete degrees, and the scheme sets are required to be optimized, and the excellent results of each level of indexes are shown in table 3.
Table 3 results of the various classes of index optimizations
As shown in table 3, in addition to having different scheme set change characteristics for each depth of water of the same property type, different scheme sets may also have different ranges of depth of water, and different property types may also exhibit completely different scheme combination types. Among them, there are 6 kinds of industrial-equipment conversion schemes at maximum, and there are 2 kinds of house-house, house-interior property and public service-house conversion schemes at minimum. That is, it follows that the set of categories exhibit dynamically preferred characteristics as the depth of water and property type change.
(b2) Selection result of loss rate maximum probability value
And (3) carrying out parameter estimation according to the scheme set selected by each water depth, and then fitting beta distribution to select the optimal loss rate value. When the water depth interval is small enough, the probability density curve reflects the probability of the x point when the water depth interval infinitely approaches a certain value. Such as the highest point of the probability density curve, the area enclosed by the corresponding infinite cells is the largest, so the larger the corresponding loss value x. The result of optimizing the commercial-house property type under 40 levels of water depths is shown in fig. 4, and the probability value of loss rate corresponding to each level of water depths is found to be obvious.
To account for the differences between the optimal value and the initial sample value, the optimal value, the statistical average, and the commercial-house loss rate sample values for each city are placed in fig. 5 for comparison. The solved optimal loss rate curve and the average loss curve are basically positioned in the middle of the sample value and have extremely similar shapes, which shows that the result of the invention obeys the general research facts. But the probability maximum is fitted to the average in the conventional mode based on the statistical distribution, which again varies in value. The probability of each loss rate obtained by the method is obviously improved, and the uncertainty in the data statistics process is reduced.
(b3) Loss curve results for all property types
The results of the 40 level depths (0.1-4.0 m) for the 10 property types calculated are shown in FIG. 6. Urban residential-interior property, business-interior property, industry-inventory, and public service-interior property loss curves remain generally highest. The interior property of a building is the most important disaster-stricken body of flood, has the characteristics of vulnerability, poor transferability and high value, and results in a region with more serious disaster-stricken loss compared with the building itself. Various buildings themselves, such as roads, public service-houses, and residential-houses, have the characteristics of strong disaster resistance and low value, and their disaster damage curves remain low.
Due to the effect of disaster reduction capability, urban flood loss increases monotonically along with the disaster intensity in a nonlinear manner, and has states of acceleration, deceleration, smoothness and the like, namely, obeys the general energy accumulation and release process. As is clear from fig. 6, the curve tends to be stationary after the water depth is 3.2m, so it is stationary in the [3.2,4.0 ] interval. And (3) using a k-means clustering algorithm to obtain the average water depth of another break point of each property type as 2.5m. Then the water depth [0.1,2.5) interval is in an acceleration state and [2.5,3.2) interval is in a deceleration state. Then the water levels 2.6m and 3.2m are inflection points of the flood loss state, i.e. abrupt points. And under different flood conditions, disaster reduction measures adopted by people are also different. If disaster relief measures should be actively taken in an acceleration state, personnel and property evacuation, acceleration and drainage and the like should be carried out, and disaster relief measures should be taken in a deceleration and stabilization state, and the rescue of government departments and the like should be actively carried out.
(b3) Discrete degree comparative analysis of optimal solution set
From the prior study, the degree of dispersion of the original data is not considered in the loss curve of the region with the index conversion data. Then the best mode set and the variance factor of the original data are compared to the present invention (fig. 7). The average variance factor for the optimal solution for all property types is 0.39, while the raw data is 0.49, the variance factor is reduced by 0.1. The selection rule of the comprehensive description optimal scheme set follows the basic characteristics of the original data, but the selection rule is obviously improved on the basis of the basic characteristics. The degree of data dispersion is reduced, and the characteristics that the data tend to be consistent in the same-proportion conversion in statistics are also met. Preference is thereby made by setting a plurality of scheme sets such that uncertainty in the reference data is reduced.
(b4) Probability comparison analysis of mean and optimum values
It can be seen from fig. 4 that each optimum loss rate is a probability maximum extracted by fitting the beta distribution through the set of schemes. By way of example, the 40 optimum probability value curves for the 2 property types shown in fig. 8, it is seen that the probability value is in an overall upward trend with water depth, especially for business-house types. The invention is more accurate in judging the loss rate of the high water level. This is similar to the actual situation, i.e. the submerged water level is high and often approaches the total disaster value, and the loss statistics is more convincing.
Conventional studies often employ the mean of the solution set as the final result, which may be a simple and quick solution. But its rationality needs to be considered. Comparing the optimal values of all loss curves with the probability values of the average (fig. 8), it is seen that the probabilities of the average are all lower than the optimal values. As compared with the average value of industry-house, the optimal value probability is improved by 52 percent; commercial-house is improved by 42%; the residence was raised by 63%. Overall, the average probability of water depth per level of 10 property types is 17.78%, the optimal value is 19.16%, and the improvement is 1.39%. While the overall phase difference is not great, the cumulative calculation of the loss data may result in loss results that are in the hundreds of thousands of dollars. Therefore, it is necessary to perform statistical distribution fitting on the loss rate samples.
(b5) Transition of early warning mode in non-data areas
The urban flood disaster forecasting and early warning mode without data is often concentrated on hydrologic features, for example, critical rainfall is formed by 3h rainfall or 6h rainfall of the whole city or region and the like and is used as an early warning mode, and urban economic space difference features are ignored. Particularly, in areas with different urban economic levels, the early warning levels should be different, for example, under the same high submerged water depth, the commercial areas with high economic value need higher early warning levels than the industrial areas. These spatial difference features are ignored due to the lack of a data-free city loss curve.
The invention forms a method for constructing a non-data urban loss evaluation curve, and the GIS is integrated to divide the calculated urban construction land into 5 types (table 1), so that the space difference characteristic of flood economic loss can be more finely simulated.
Claims (3)
1. A method for determining an optimal loss curve of a non-material city based on double-layer target optimization is characterized by comprising the following steps: the method comprises the following steps:
s1: for research cities, m reference cities are selected, and a loss rate matrix R consisting of the m reference cities is constructed 0 ：
S2: k characteristic indexes are selected, and n different combination schemes are formed through the K characteristic indexes:
in the formula (3), the amino acid sequence of the compound,representing the number of schemes for K characteristic indexes to select K index combinations;
s3: feature integrated values of the study city and the reference city under n combination schemes are calculated respectively:
ream CI j Representing the feature integrated value of the research city under the j scheme, j=1 to n; order theRepresenting the feature integrated value of the ith reference city under the jth scheme, i=1 to m; wherein, when j=1 to K, the scheme is a single index scheme, and the index value of the single index scheme is the integrated value; when j=K+1-n, the scheme is a multi-index scheme, and index values of the multi-index scheme are converted into comprehensive values through index weights;
in the step, for the jth multi-index scheme containing S indexes, a projection pursuit model based on chaotic particle swarm optimization is adopted to calculate the weight, and the specific calculation flow is as follows:
s3-1: the ith index value I for the ith city is The city here includes a study city and m reference cities, i=1 to m+1, s=1 to S, and I is calculated is Standard value of (2)
Wherein, the formula (6) is used for processing the larger and more optimal type index, and the formula (7) is used for processing the smaller and more optimal type index;
s3-2: calculating the projection integrated value CI of the ith city under the jth scheme by the formula (8) ij ：
In the formula (8), i=1 to m+1, j=k+1 to n, W S Projection weights which can be optimized for the index;
s3-3: calculating a projection objective function Q (W) by the method (9) S ) And the constraint is set as close to 1 as possible by equation (10):
maxQ(W S )＝S D |R| (9)
here, S D For projection integrated value CI ij Standard deviation of (2); r is projection integrated value CI ij Correlation coefficients with experience levels;
s4: let lambda set ij Is the ith th Reference city j th Transfer coefficient of scheme, letObtaining a transfer coefficient matrix A of m multiplied by n combination schemes:
s5: based on the above, a m×n order study city loss rate matrix R is calculated:
s6: obtaining an optimal characteristic scheme based on a minimum optimization principle of a variation coefficient by using a loss rate matrix R
S7: according to the best modeThe following column vector is fitted with a beta distribution curve, and the maximum probability corresponding value of the curve is extracted as the optimal loss rate R;
s8: and repeating the steps S1 to S7, and calculating the optimal loss value of each property type under each water depth level, so as to obtain a water depth-loss rate relation curve of each property type.
2. The method for determining an optimal loss curve based on a double-layer objective optimized material-free city of claim 1, wherein: in the step S6: optimal characteristic scheme based on principle of minimal optimization of variation coefficientThe specific flow of (a) is as follows:
s6-1: calculating a variation coefficient CV of each column vector of the loss rate matrix R from the formula (13) j And the variation coefficient set CV is formed by the formula (14):
wherein ,uj Mean value of j-th group column vector, sigma j Variance for the j-th set of column vectors;
s6-2: extracting a column vector with the smallest variation coefficient from the formula (15), wherein the corresponding s-th scheme is the optimal scheme
3. The method for determining an optimal loss curve based on a double-layer objective optimized material-free city of claim 1, wherein: the specific flow in the step S7 is as follows:
s7-1: according to the distance estimation methodThe value of the m sample loss in the water depth is subjected to beta distribution parameter estimation, and the beta distribution overall average E (R) under the water depth is calculated by the formula (18) and the formula (19) respectively ij ) Sum variance Var (R) ij )：
Wherein μ and σ are the mean and variance of the sample loss rate, respectively;
alpha and beta are calculated from the following formula:
wherein ,for the distance estimation of the loss curve alpha +.>Distance estimator for β;
s7-2: and determining a beta distribution curve according to the distance estimation parameters alpha and beta, and extracting a maximum probability corresponding value as an optimal loss rate R.
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