A method for evaluating the stability of a secondary suspended river

Abstract

The present invention provides a method for evaluating the stability of a secondary suspended river, and belongs to the technical field of water conservancy engineering based on computer data processing. First, a number of evaluation indicators related to the stability of a secondary suspended river are obtained, a secondary suspended river stability evaluation index system is constructed, and each evaluation indicator is normalized; then, a wavelet transform correlation analysis method is used to analyze the evaluation indicators in the secondary suspended river stability evaluation index system, core indicators are screened out, and a core evaluation index system is constructed; finally, based on the constructed evolutionary algorithm optimized projection pursuit TOPSIS comprehensive evaluation model, the core evaluation indicator weight is multiplied by the core evaluation indicator data and then input into the model to divide the stability level for the evaluation object. The present invention uses a wavelet transform correlation analysis method to screen the initial evaluation indicators and constructs a more streamlined core evaluation index system; the design of the comprehensive evaluation model reduces the interference of human factors and improves the objectivity of the evaluation.

Description

Technical Field

[0001] The invention belongs to the technical field of water conservancy engineering based on computer data processing, and in particular relates to a method for evaluating the stability of a secondary suspended river. Background Art

[0002] The secondary suspended river phenomenon is the result of long-term siltation and unharmonious water-sediment relationship in the river. It is manifested in the high shoal lip of the main channel of the river, the low-lying embankment root, and the obvious horizontal gradient between the shoal lip and the embankment root. This phenomenon not only aggravates the flood threat downstream of the river, but also leads to the instability of the river morphology, increasing the risk of breach and diversion. By evaluating the stability of the secondary suspended river, potential safety hazards and risk points can be discovered in a timely manner, providing strong support for early warning and emergency work; once abnormal conditions in the river are found, the emergency plan can be quickly activated and effective measures can be taken to prevent the situation from escalating and reduce losses. Therefore, the development of a secondary suspended river stability evaluation method can provide strong technical support and decision-making basis for river management. The existing secondary suspended river stability evaluation technologies are mainly divided into the following three types:

[0003] 1. Geological survey: Through detailed geological survey, important information about the geological structure, stratigraphic lithology, soil properties and groundwater conditions of the secondary hanging river area can be obtained. This information is crucial to understanding the formation mechanism, evolution process and current stability of the secondary hanging river. A systematic geological survey of the secondary hanging river area was conducted using 3S technology (remote sensing technology RS, geographic information system GIS and global positioning system GPS) to manually determine the stability of different sections of the secondary hanging river.

[0004] 2. Environmental monitoring: By monitoring hydrological parameters such as precipitation, flood flow and sediment content in the secondary hanging river area, the impact of floods on the stability of the secondary hanging river is evaluated using the monitoring data; at the same time, geological parameters such as river morphology and riverbed elevation are monitored to evaluate the evolution trend and stability status of the secondary hanging river.

[0005] 3. Comprehensive evaluation method: The comprehensive evaluation method is a means of comprehensively evaluating the stability of the secondary suspension river by combining the results of geological survey, environmental monitoring and data analysis. Commonly used comprehensive evaluation methods include fuzzy comprehensive evaluation method, hierarchical analysis method, grey correlation analysis method, etc. These methods can comprehensively consider multiple influencing factors and quantitatively analyze and evaluate the stability of the secondary suspension river. For example, the fuzzy comprehensive evaluation method can be used to quantitatively analyze the crust stability, embankment foundation stability and river geomorphological stability of the secondary suspension river, and comprehensively consider future earthquakes, river channel front and back differences, river potential and river type, historical breaches, foundation soil liquefaction and seepage deformation, etc., to find the most unstable dangerous point.

[0006] In the comprehensive evaluation technology of the stability of the secondary suspended river channel, the comprehensive evaluation method can comprehensively consider the evaluation indicators that affect the stability of the secondary suspended river, and use data analysis methods to obtain the stability of different sections of the secondary suspended river. Compared with the two technologies of geological survey and environmental monitoring, the evaluation results are more objective and accurate. However, the existing comprehensive evaluation technology cannot effectively distinguish the evaluation indicators when facing multiple evaluation objects and high-dimensional evaluation indicators, resulting in low accuracy of the evaluation results. Summary of the invention

[0007] In order to solve the deficiencies of the prior art, the present invention proposes a secondary suspended river stability evaluation method, which includes the following process:

[0008] S1, obtaining several evaluation indicators related to the stability of the secondary hanging river channel, constructing a secondary hanging river stability evaluation indicator system, and normalizing each evaluation indicator;

[0009] S2, using the wavelet transform correlation analysis method to analyze the evaluation indicators in the secondary hanging river stability evaluation index system, screen out the core indicators, and construct the core evaluation index system;

[0010] S3, based on the projection pursuit-TOPSIS comprehensive evaluation model optimized by the evolutionary algorithm, the core evaluation index weight is multiplied by the core evaluation index data and then input into the model to classify the stability level of the evaluation object; the processing process of the projection pursuit-TOPSIS comprehensive evaluation model is as follows:

[0011] The indicators included in the core evaluation index system are projected onto a one-dimensional space to form projection indicators. The projection direction is optimized using an evolutionary algorithm so that the projection indicators can reflect the differences in river stability to the greatest extent. The optimized weights are multiplied by the standardized evaluation index data to construct a weighted decision matrix. In the weighted decision matrix, the maximum and minimum values ​​of each indicator are found as positive ideal solutions and negative ideal solutions, respectively. The Euclidean distance of each evaluation object to the positive ideal solution and the negative ideal solution is calculated, and then the proximity, that is, the degree of closeness to the ideal solution, is calculated. The evaluation objects are sorted according to the proximity to obtain the river stability level of the river section.

[0012] Preferably, each evaluation index is normalized in S1, and the specific process is as follows:

[0013] According to the correlation between the evaluation index and the stability of the secondary suspended river, the evaluation index is divided into extremely large index and extremely small index. The larger the value of the extremely large index is, the higher the stability of the secondary suspended river is; the smaller the value of the extremely small index is, the higher the stability of the secondary suspended river is.

[0014] For extremely large and extremely small indicators, formulas (1) and (2) are used for normalization respectively:

[0015]

[0016] Among them, x max is the maximum value of a single evaluation index data, x min is the minimum value of a single evaluation index data, x norm It is the normalized indicator data.

[0017] Preferably, the secondary suspended river stability evaluation index system in S1 includes 8 evaluation indicators, namely, horizontal gradient of beach, annual runoff, annual sediment transport, annual sediment coefficient, water flow scouring intensity during flood season, ditch development speed, levee height and levee width;

[0018] The beach horizontal gradient data is obtained by inputting the satellite remote sensing image of the secondary suspended river into the geographic information system (GIS) software to obtain the elevation information of the river cross section, and then calculating the beach horizontal gradient; the annual runoff data and annual sediment transport data are obtained through the hydrological station; the annual sediment coefficient is obtained by calculating the annual runoff and annual sediment transport; the flood season water flow scouring intensity and gully development speed are obtained by inputting the satellite remote sensing image of the secondary suspended river into the geographic information system (GIS) software; the levee height and levee width are obtained by total station measurement.

[0019] Preferably, the specific process of S2 is:

[0020] S21, the normalized evaluation index obtained in S1 is subjected to wavelet transformation. The specific formula is as follows:

[0021]

[0022] Among them, X i is the i-th evaluation index in the evaluation index system, t is the evaluation index data index, ψ(t) is the wavelet transform function, W i (a, b) is the wavelet coefficient of the i-th evaluation index, a is the scale of the wavelet transform and b is the translation;

[0023] S22, calculate the correlation coefficient of the wavelet coefficients of different evaluation indicators; since the indicators in the evaluation indicator system have non-stationary time series data, the cross-correlation function is used to calculate the wavelet coefficients of different evaluation indicators, as follows:

[0024]

[0025] Where τ is the time delay, R ij (a, τ) is the evaluation index X i And the evaluation index X j The correlation coefficient between

[0026] S23, eliminate evaluation indicators with collinearity and build a core evaluation indicator system.

[0027] Preferably, the specific process of S23 is:

[0028] Based on the wavelet coefficients of different evaluation indicators obtained by S22, the sum of the wavelet coefficients of each evaluation indicator is calculated. For the i-th evaluation indicator, its wavelet coefficient S i The formula for calculating the sum is as follows:

[0029]

[0030] Traverse the evaluation indicators, if the evaluation indicator X i And the evaluation index X j The wavelet coefficient between is greater than the preset threshold ∈, which means that X i and xj There is multicollinearity between i and X j The wavelet coefficients and the evaluation indicators greater than the preset threshold are removed from the evaluation indicator system, and finally M core evaluation indicators K = {K1, ..., K M}; M core evaluation indicators constitute the core evaluation indicator system.

[0031] Preferably, the specific process of the projection pursuit-TOPSIS comprehensive evaluation model in S3 includes:

[0032] S31, initialization of projection direction; randomly generate a set of projection direction vectors α=(β1,β m , …, β M ), where β m is the projection direction coefficient of the mth core evaluation index;

[0033] S32, calculating the projection value: calculating the projection value of the core evaluation index of the t-th evaluation object according to the projection direction α, where the evaluation object is different river sections, and the specific calculation formula is as follows:

[0034]

[0035] in, is the value of the mth core evaluation indicator of the tth evaluation object;

[0036] S33, optimizing the projection direction based on the established projection value optimization mathematical model, and iteratively optimizing the projection direction α using an evolutionary algorithm to obtain the projection direction α that minimizes the fitness function Fitness * ;

[0037] S34, construct a weighted decision matrix; *Multiply it with the core evaluation index to obtain the weighted decision matrix V(m, t):

[0038]

[0039] S35, select the maximum value of each core indicator in V(m, t) to form a positive ideal solution vector Select the minimum value of each core indicator in V(m, t) to form a negative ideal solution vector

[0040] S36, calculating the Euclidean distance of each evaluation object to the positive ideal solution and the negative ideal solution;

[0041] S37, calculating the cosine distance between each evaluation object and the positive ideal solution and the negative ideal solution, the specific calculation formula is as follows:

[0042]

[0043] Among them, ||·|| is the symbol for calculating the vector modulus, K t is the core evaluation index vector of the tth evaluation object, is the cosine distance between the tth evaluation object and the positive ideal solution, is the cosine distance between the tth evaluation object and the negative ideal solution;

[0044] S38, calculate the proximity of each evaluation object according to the Euclidean distance and the cosine distance, and the specific calculation formula is as follows:

[0045]

[0046] Among them, C t is the proximity of the tth evaluation object, |·| is the absolute value operator;

[0047] S39, classifying the evaluation objects into stability levels according to the proximity of each evaluation object and a set threshold.

[0048] Preferably, the established projection value optimization mathematical model is specifically:

[0049] Construct the following objective function f:

[0050] f=σ z D z

[0051] Among them, S z is the standard deviation of all projection values, D z is the local density of the t-th projection value, and the specific calculation formulas for the two are as follows:

[0052]

[0053] Where T is the number of evaluation objects, is the mean of the projection values ​​of all evaluation objects; standard deviation σ z The larger the value, the higher the dispersion of the projection value in one-dimensional space, that is, the more obvious the difference in stability between different river sections; H is the bandwidth of the Gaussian kernel, zρ is z t The ρth neighborhood element of , γ is the size of the domain element, and ||·|| is the operator for finding the modulus length; D z The larger the value, the fewer the neighboring elements of zt in one-dimensional space, the smaller the local density, and the smaller the z t The more obvious the difference between the stability of the represented river channel and the stability of other river channels;

[0054] Design the following fitness function Fitness:

[0055]

[0056] in, Equal to 10 -6 , to ensure that the denominator of the fitness function is not 0.

[0057] Preferably, in S33, an evolutionary algorithm is used to iteratively optimize the projection direction α, specifically:

[0058] S331, initialize the population; based on the projection direction α The conditions are as follows: the population size is initialized to N, Population = {P1, P2, ..., P N}, where the nth individual in the population

[0059] S332, randomly divide Population into two scales Population, one is the constrained population Pop co , and the other is the unconstrained population Pop nco ;

[0060] S333, Pop co and Pop nco Substitute the population individuals in the fitness function Fitness to obtain the fitness of each population individual;

[0061] S334, Pop co and Pop nco Perform binary tournament selection, crossover and mutation operations respectively to obtain the offspring population Off co and Off nco ;

[0062] S335, set Off co and Off ncoSubstitute the population individuals in the fitness function Fitness to obtain the fitness of each population individual;

[0063] S336, use natural selection operator to update the unconstrained population; set Off co 、Off nco and Pop nco Enter the environment selection operator to obtain the next generation of unconstrained population and replace Pop nco Individuals of the original population;

[0064] S337, Check Off co and Off nco Do the individuals in the population satisfy If this constraint is not met, the fitness of the individuals in the population that do not meet the constraint will be doubled.

[0065] S338, use the natural selection operator to update the constrained population; set Off co 、Off nco and Pop co Input the environment selection operator to obtain the next generation of constrained population and replace Pop co Individuals of the original population;

[0066] S339, determine whether the maximum number of evaluations has been reached. If not, repeat steps S333 to S338 until the maximum number of evaluations is reached and output Pop co ;

[0067] Pop co The population individual with the smallest fitness is taken as the best projection direction α * .

[0068] Compared with the prior art, the present invention has the following beneficial effects:

[0069] 1. Comprehensiveness of the stability evaluation of secondary suspended rivers: By constructing a system of eight evaluation indicators, including the horizontal gradient of the beach, annual runoff, annual sediment transport, annual sediment coefficient, water flow scouring intensity during flood season, ditch development speed, levee height and levee width, it comprehensively covers multiple key factors affecting the stability of secondary suspended rivers, making the evaluation results more comprehensive and systematic, and better reflecting the actual conditions of the river channel.

[0070] 2. Ability to effectively eliminate irrelevant indicators: The wavelet transform correlation analysis method is used to screen the initial evaluation indicators, and evaluation indicators with significant multicollinearity are proposed to construct a more streamlined core evaluation indicator system, thus avoiding the interference of redundant information on the river stability evaluation results.

[0071] 3. Improved the objectivity of the evaluation results: The projection pursuit comprehensive evaluation model was optimized using an evolutionary algorithm. The high-dimensional evaluation indicators were projected into one-dimensional space through projection pursuit technology, and the projection direction was optimized in combination with the evolutionary algorithm, so that the projection indicators could reflect the differences in river stability to the greatest extent. The optimized weights were multiplied by the standardized evaluation indicator data and used as the input of TOPSIS, which could highlight the differences between the evaluation indicators, reduce the interference of human factors, and improve the objectivity of the evaluation. At the same time, the evolutionary algorithm adopted a parallel search mode of constrained search and unconstrained search, which could explore the feasible domain in the target space as much as possible, obtain the best projection direction, and further improve the accuracy of the comprehensive evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] In order to more clearly illustrate the technical solutions of the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, what is described below is only one embodiment of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0073] Figure 1 This is the overall process of the secondary suspended river stability evaluation method proposed by the present invention;

[0074] Figure 2 It is the overall flow chart of wavelet transform correlation analysis of evaluation indicators;

[0075] Figure 3 It is the overall flow chart of iterative optimization of projection direction using evolutionary algorithm;

[0076] Figure 4 Schematic diagram of visualization of proximity score in an embodiment of the present invention. DETAILED DESCRIPTION

[0077] The present invention proposes a method for evaluating the stability of a secondary suspended river. The overall process is as follows: Figure 1As shown in the figure. Firstly, the evaluation index system of the stability of the secondary suspended river channel is constructed, which can include eight evaluation indicators: the horizontal gradient of the beach, annual runoff, annual sediment transport, annual sediment coefficient, water flow scouring intensity during the flood season, ditch development speed, levee height and levee width; secondly, the wavelet transform correlation analysis method is used to analyze the evaluation indicators in the evaluation index system of the stability of the secondary suspended river channel, screen out the core indicators, and construct the core evaluation index system. Finally, a projection pursuit-TOPSIS comprehensive evaluation model based on evolutionary algorithm optimization is constructed. The indicators included in the core evaluation index system are projected into one-dimensional space to form projection indicators. The projection direction is optimized by evolutionary algorithm so that the projection indicators can reflect the differences in river stability to the greatest extent. The optimized weights are multiplied with the standardized evaluation index data to construct a weighted decision matrix. In the weighted decision matrix, the maximum and minimum values ​​of each indicator are found as positive ideal solutions and negative ideal solutions respectively. The Euclidean distance of each evaluation object to the positive ideal solution and the negative ideal solution is calculated, and then the proximity (that is, the degree of closeness to the ideal solution) is calculated. The evaluation objects are sorted according to the proximity to obtain the river stability level of the river section.

[0078] 1. Construct a secondary suspended river channel stability evaluation index system

[0079] Construct a secondary suspended river channel stability evaluation index system. In this embodiment, a total of 8 evaluation indicators are obtained, including the beach horizontal gradient, annual runoff, annual sediment transport, annual sediment coefficient, flood season water flow scouring intensity, gully development speed, levee height and levee width. First, collect the data of each evaluation indicator. The beach horizontal gradient data is obtained by inputting the satellite remote sensing image of the secondary suspended river into the geographic information system (GIS) software to obtain the elevation information of the river cross section, and then calculate the beach horizontal gradient; the annual runoff data and annual sediment transport data are obtained through the hydrological station; the annual sediment coefficient is obtained by calculating the annual runoff and annual sediment transport; the flood season water flow scouring intensity and gully development speed are obtained by inputting the satellite remote sensing image of the secondary suspended river into the geographic information system (GIS) software; the levee height and levee width are obtained by total station measurement; secondly, normalize each evaluation indicator to unify the dimension;

[0080] The evaluation indicators in the evaluation index system for the stability of secondary suspended river channels have different dimensions. When these indicators with different dimensions are directly compared or calculated, large errors will occur. Normalization can convert these indicators into dimensionless values, thereby eliminating the impact of dimensions on the results. According to the correlation between the evaluation indicators and the stability of secondary suspended river channels, the evaluation indicators are divided into extremely large indicators and extremely small indicators. Among them, annual runoff, annual sediment transport, annual sediment coefficient, flood season water flow scouring intensity and gully development speed are extremely large indicators. The larger the values ​​of these indicators, the higher the stability of the secondary suspended river. The horizontal gradient of the beach and the width of the levee are extremely small indicators. The smaller the values ​​of these indicators, the higher the stability of the secondary suspended river. Formulas (1) and (2) are used to normalize the extremely large indicators and the extremely small indicators respectively:

[0081]

[0082] Among them, x max is the maximum value of a single evaluation index data, x min is the minimum value of a single evaluation index data, x norm It is the normalized indicator data.

[0083] 2. Constructing the core evaluation index system of secondary hanging river

[0084] The wavelet transform correlation analysis method was used to conduct correlation analysis on the evaluation indicators in the constructed secondary hanging river channel stability evaluation index system, eliminate the evaluation indicators with significant multicollinearity, and construct the core evaluation index system.

[0085] There may be multicollinearity between the evaluation indicators in the evaluation indicator system. One of the basic assumptions of the comprehensive evaluation method is that the evaluation indicators are independent of each other. When the evaluation indicators are highly correlated, multicollinearity will occur. When it is serious, different evaluation indicators characterize the same characteristics of the stability of the secondary hanging river channel, making it very difficult to determine the influence of each individual evaluation indicator on the stability of the secondary hanging river channel. In order to eliminate the evaluation indicators with multicollinearity in the constructed evaluation indicator system and eliminate redundant information, the present invention performs wavelet transform correlation analysis on the evaluation indicators. The process is as follows: Figure 2 shown.

[0086] Wavelet transform correlation analysis is a method that combines wavelet transform and correlation analysis. It aims to reveal the relationship between different evaluation indicators at different time scales. It is very suitable for analyzing non-stationary signals. The specific steps are as follows:

[0087] S1, the normalized evaluation index is subjected to wavelet transform, and the specific formula is as follows:

[0088]

[0089] Among them, X i is the i-th evaluation index in the evaluation index system, t is the evaluation index data index, ψ(t) is the wavelet transform function, W i (a, b) is the wavelet coefficient of the i-th evaluation index, a is the scale of the wavelet transform and b is the translation;

[0090] S2, calculate the correlation coefficient of the wavelet coefficients of different evaluation indicators; since the annual runoff, annual sediment transport, annual sediment coefficient, flood season water flow scouring intensity and ditch development speed in the evaluation indicator system are non-stationary time series data, the present invention uses the cross-correlation function to calculate the wavelet coefficients of different evaluation indicators, as follows:

[0091]

[0092] Where τ is the time delay, R ij (a, τ) is the evaluation index X i And the evaluation index X j The correlation coefficient between

[0093] S3, eliminate the evaluation indicators with collinearity and construct the core evaluation indicator system, as follows:

[0094] 1) Based on the wavelet coefficients of different evaluation indicators obtained by S2, calculate the sum of the wavelet coefficients of each evaluation indicator. For the i-th evaluation indicator, its wavelet coefficient and S i The calculation formula is as follows:

[0095]

[0096] 2) Traverse the evaluation indicators. If the evaluation indicator X i And the evaluation index X j The wavelet coefficient between is greater than the preset threshold ∈, which means that X i and X j There is multicollinearity between i and X j The medium and small wavelet coefficients and large evaluation indicators are removed from the evaluation indicator system; multicollinearity will reduce the significance of the evaluation indicators for river stability, so it is necessary to remove indicators with multicollinearity to delete redundant information; finally, M core evaluation indicators K = {K1, ..., K M}, in this embodiment, M≤8; M core evaluation indicators constitute the core evaluation indicator system.

[0097] 3. Projection pursuit-TOPSIS comprehensive evaluation model construction and data processing

[0098] In order to highlight the differences between the core evaluation indicators in the constructed core evaluation indicator system and improve the accuracy of comprehensive evaluation, the present invention adopts the projection pursuit method to calculate the weights of the core evaluation indicators; the projection pursuit method is an effective method for processing and analyzing high-dimensional data. The method projects the high-dimensional data onto a low-dimensional subspace and finds the projection direction that best reflects the structure or characteristics of the original data, thereby achieving a comprehensive evaluation of the data. The projection pursuit method has the ability to process high-dimensional data and can reveal the complex relationship between the data; at the same time, the method is driven by objective data and does not require manual weight setting, so the weights of the core evaluation indicators obtained are more objective and accurate; the core evaluation indicator weights are multiplied by the core evaluation indicator data and then input into the TOPSIS comprehensive evaluation model to obtain the secondary hanging river channel stability evaluation results, and the specific steps are as follows:

[0099] S1, projection direction initialization; randomly generate a set of projection direction vectors α=(β1, β m , …, β M ), where β m is the projection direction coefficient of the mth core evaluation index;

[0100] S2, calculate the projection value; calculate the projection value of the core evaluation index of the tth evaluation object (river section) according to the projection direction α. ​​The specific calculation formula is as follows:

[0101]

[0102] in, is the value of the mth core evaluation indicator of the tth evaluation object;

[0103] S3, optimizing the projection direction; the accuracy of the projection pursuit method is affected by the projection direction, because the projection direction can best reflect the structure or characteristics of the core evaluation index data. In order to obtain the optimal projection direction, the present invention designs an evolutionary algorithm to optimize the projection direction. The specific steps are as follows:

[0104] Establish a mathematical model for optimizing projection value; design an objective function to evaluate the projection value z t When reflecting the degree of river channel stability difference, it is necessary to consider how the projection value can distinguish the stability differences between different evaluation objects as much as possible; therefore, the present invention constructs the following objective function f:

[0105] f=σ z D z (7)

[0106] Among them, S z is the standard deviation of all projection values, D z is the local density of the t-th projection value, and the specific calculation formulas for the two are as follows:

[0107]

[0108] Where T is the number of evaluation objects, is the mean of the projection values ​​of all evaluation objects; standard deviation σ z The larger the value is, the higher the dispersion of the projection value in one-dimensional space is, that is, the more obvious the difference in stability between different river sections is; H is the bandwidth of the Gaussian kernel, z ρ For z t The ρth neighborhood element of , γ is the size of the domain element, and ||·|| is the operator for finding the modulus length; D z The larger the z t The fewer the neighborhood elements in one-dimensional space, the smaller the local density, and z t The more obvious the difference between the stability of the represented river channel and the stability of other river channels;

[0109] Because the evolutionary algorithm is suitable for solving minimization problems, the following fitness function Fitness is designed:

[0110]

[0111] in Equal to 10 -6 , ensure that the denominator of the fitness function is not 0;

[0112] The evolutionary algorithm is used to iteratively optimize the projection direction α to obtain Fitness The smallest projection direction α*;

[0113] S4, construct a weighted decision matrix; multiply α* by the core evaluation index to obtain the weighted decision matrix V(m, t):

[0114]

[0115] S5, select the maximum value of each core indicator in V(m, t) to form a positive ideal solution vector Select the minimum value of each core indicator in V(m, t) to form a negative ideal solution vector

[0116] S6, calculate the Euclidean distance of each evaluation object to the positive ideal solution and the negative ideal solution. The specific calculation formula is as follows:

[0117]

[0118] in, is the distance from the tth evaluation object to the positive ideal solution, is the distance from the tth evaluation object to the negative ideal solution;

[0119] S7, calculate the cosine distance between each evaluation object and the positive ideal solution and the negative ideal solution. Different from the traditional TOPSIS comprehensive evaluation method, the present invention introduces the cosine distance to measure the similarity between each evaluation object and the positive ideal solution and the negative ideal solution based on the TOPSIS model. The cosine distance mainly focuses on the similarity of the two vectors in direction, rather than their absolute value or length. This means that even if the lengths of the two vectors are very different, as long as their directions are similar, the cosine similarity will be very high. This feature makes the cosine distance very effective in processing high-dimensional evaluation indicators, because the evaluation indicator data will have certain zero values, and these zero values ​​will be misleading for the method based on Euclidean distance. The specific calculation formula is as follows:

[0120]

[0121] Among them, ||·|| is the symbol for calculating the vector modulus, K t is the core evaluation index vector of the tth evaluation object, is the cosine distance between the tth evaluation object and the positive ideal solution, is the cosine distance between the tth evaluation object and the negative ideal solution;

[0122] S8, calculate the proximity of each evaluation object according to the Euclidean distance and cosine distance. The specific calculation formula is as follows:

[0123]

[0124] Among them, C t is the proximity of the tth evaluation object, |·| is the absolute value operator;

[0125] S9, classifying the evaluation objects into stability levels according to the proximity of each evaluation object and a set threshold.

[0126] Among them, the convergence speed of the evolutionary algorithm determines the optimization accuracy of the projection vector optimization problem. The faster the convergence speed of the evolutionary algorithm, the easier it is to find the global optimal solution of the projection vector optimization problem. However, the projection direction constraint in the projection vector optimization problem The search of the evolutionary algorithm in the search space is limited. Therefore, the evolutionary algorithm must avoid the infeasible domain of the search space while searching for the optimal projection vector, resulting in a slow convergence speed of the evolutionary algorithm. Therefore, the present invention improves the traditional evolutionary algorithm and proposes a multi-population collaborative search algorithm, which divides the population into a constrained population and an unconstrained population to explore the projection vector optimization problem respectively, wherein the constrained population solves the original projection vector optimization problem, and the unconstrained population ignores the projection direction constraint to solve the unconstrained projection vector optimization problem. Through the knowledge transfer between the constrained population and the unconstrained population, the constrained population is guided to a better feasible domain, thereby improving the convergence speed of the constrained population. The specific process is as follows Figure 3 As shown, the specific steps are as follows:

[0127] S31, initialize the population; based on the projection direction α The conditions are as follows: the population size is initialized to N, Population = {P1, P2, ..., P N}, where the nth individual in the population

[0128] S32, randomly divide Population into two scales Population, one is the constrained population Pop co , and the other is the unconstrained population Pop nco ;

[0129] S33, Pop co and Pop nco Substitute the population individuals in the fitness function Fitness to obtain the fitness of each population individual;

[0130] S34, Pop co and Pop nco Perform binary tournament selection, crossover and mutation operations respectively to obtain the offspring population Off co and Off nco ;

[0131] S35, set Off co and Off nco Substitute the population individuals in the fitness function Fitness to obtain the fitness of each population individual;

[0132] S36, use the natural selection operator to update the unconstrained population; set Off co 、Off nco and Pop nco Enter the environment selection operator to obtain the next generation of unconstrained population and replace Pop nco Individuals of the original population;

[0133] S37, Check Off co and Off nco Do the individuals in the population satisfy If this constraint is not met, the fitness of the individuals in the population that do not meet the constraint will be doubled.

[0134] S38, use the natural selection operator to update the constrained population; set Off co 、Off nco and Pop co Input the environment selection operator to obtain the next generation of constrained population and replace Pop co Individuals of the original population;

[0135] S39, determine whether the maximum number of evaluations has been reached. If not, repeat steps S33 to S38 until the maximum number of evaluations is reached and output Pop co ;

[0136] Pop co The population individual with the smallest fitness is taken as the best projection direction α * .

[0137] 4. Experimental Results

[0138] The method proposed in the present invention is used to comprehensively evaluate the stability of 10 river sections of a secondary suspended river in the lower reaches of the Yellow River; the normalized evaluation index data of the 10 river sections are shown in Table 1:

[0139] Table 1 Normalized evaluation index data of 10 river sections

[0140]

[0141] The wavelet correlation analysis method used in the present invention is used to analyze the data in Table 1 to obtain the core evaluation index data as shown in Table 2:

[0142] Table 2 Core evaluation index data

[0143]

[0144]

[0145] The annual sediment coefficient was eliminated as a redundant variable, and the remaining indicators in the evaluation index system, namely, the horizontal gradient of the beach, annual runoff, annual sediment transport, water flow scouring intensity during the flood season, gully development speed, levee height and levee width, constituted the core evaluation index system.

[0146] The core evaluation index data shown in Table 2 are input into the projection pursuit-TOPSIS comprehensive evaluation model based on evolutionary algorithm optimization proposed in the present invention, and the projection values ​​of each core evaluation index obtained are shown in Table 3.

[0147] Table 3 Projection values ​​of each core evaluation index

[0148] River section number Beach horizontal gradient 1 0.1429 2 0.2411 3 0.0714 4 0.4571 5 0.2857 6 0.2286 7 0.3214 8 0.0893 9 0.5214 10 0.3643

[0149] As shown in Table 4 and Figure 4 As shown, the proximity scores obtained by the present invention can be evenly distributed in the range of 0 to 1, indicating that the method proposed by the present invention can effectively distinguish the differences in stability of different river sections.

[0150] Using the four intervals of 0.76 to 1 as the stability range, the stability of sections 3 and 9 can be divided into one level, the stability of sections 6, 1 and 5 can be divided into one level, the stability of sections 4, 2, 7 and 10 can be divided into one level, and section 9 can be classified into a single stability level.

[0151] Table 4 Proximity scores of 10 river sections

[0152] River section number Proximity score Ranking 1 0.4757 6 2 0.5714 5 3 0 10 4 0.7071 4 5 0.5 7 6 0.4444 8 7 0.6154 3 8 0.1429 9 9 0.8165 1 10 0.5385 2

[0153] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

[0154] Although the above describes the specific implementation methods of the present invention, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A method for evaluating the stability of a secondary suspended river, characterized in that: The process includes: S1, obtaining several evaluation indicators related to the stability of the secondary hanging river channel, constructing a secondary hanging river stability evaluation indicator system, and normalizing each evaluation indicator; The secondary suspended river stability evaluation index system includes 8 evaluation indicators, including the horizontal gradient of the beach, annual runoff, annual sediment transport, annual sediment coefficient, water flow scouring intensity during flood season, gully development speed, levee height and levee width; S2, using the wavelet transform correlation analysis method to analyze the evaluation indicators in the secondary hanging river stability evaluation index system, screen out the core indicators, and construct the core evaluation index system; S3, based on the projection pursuit-TOPSIS comprehensive evaluation model optimized by the evolutionary algorithm, the core evaluation index weight is multiplied by the core evaluation index data and then input into the model to classify the stability level of the evaluation object; the processing process of the projection pursuit-TOPSIS comprehensive evaluation model is as follows: The indicators included in the core evaluation index system are projected onto a one-dimensional space to form projection indicators. The projection direction is optimized using an evolutionary algorithm so that the projection indicators can reflect the differences in river channel stability to the greatest extent. The optimized weights are multiplied by the standardized evaluation index data to construct a weighted decision matrix. In the weighted decision matrix, the maximum and minimum values ​​of each indicator are found as positive ideal solutions and negative ideal solutions, respectively. The Euclidean distance of each evaluation object to the positive ideal solution and the negative ideal solution is calculated, and then the proximity, that is, the degree of closeness to the ideal solution, is calculated. The evaluation objects are sorted according to the proximity to obtain the channel stability level of the river section.

2. A method for evaluating the stability of a secondary suspended river as claimed in claim 1, characterized in that: In S1, each evaluation index is normalized, and the specific process is as follows: According to the correlation between the evaluation index and the stability of the secondary suspended river channel, the evaluation index is divided into extremely large index and extremely small index. The larger the value of the extremely large index is, the higher the stability of the secondary suspended river is; the smaller the value of the extremely small index is, the higher the stability of the secondary suspended river is. For extremely large and extremely small indicators, formulas (1) and (2) are used for normalization respectively: Among them, x max is the maximum value of a single evaluation index data, x min is the minimum value of a single evaluation index data, x norm It is the normalized indicator data.

3. A method for evaluating the stability of a secondary suspended river as claimed in claim 1, characterized in that: The beach horizontal gradient data is obtained by inputting the satellite remote sensing image of the secondary suspended river into the geographic information system (GIS) software to obtain the elevation information of the river cross section, and then calculating the beach horizontal gradient; the annual runoff data and annual sediment transport data are obtained through the hydrological station; the annual sediment coefficient is obtained by calculating the annual runoff and annual sediment transport; the flood season water flow scouring intensity and gully development speed are obtained by inputting the satellite remote sensing image of the secondary suspended river into the geographic information system (GIS) software; the levee height and levee width are obtained by total station measurement.

4. A method for evaluating the stability of a secondary suspended river as claimed in claim 1, characterized in that: The specific process of S2 is: S21, the normalized evaluation index obtained in S1 is subjected to wavelet transformation. The specific formula is as follows: Among them, X i is the i-th evaluation index in the evaluation index system, t is the evaluation index data index, ψ(t) is the wavelet transform function, W i (a, b) is the wavelet coefficient of the i-th evaluation index, a is the scale of the wavelet transform and b is the translation; S22, calculate the correlation coefficient of the wavelet coefficients of different evaluation indicators; since the indicators in the evaluation indicator system have non-stationary time series data, the cross-correlation function is used to calculate the wavelet coefficients of different evaluation indicators, as follows: Where τ is the time delay, R ij (a,τ) is the evaluation index X i And the evaluation index X j The correlation coefficient between S23, eliminate evaluation indicators with collinearity and build a core evaluation indicator system.

5. A method for evaluating the stability of a secondary suspended river as claimed in claim 4, characterized in that: The specific process of S23 is as follows: Based on the wavelet coefficients of different evaluation indicators obtained by S22, the sum of the wavelet coefficients of each evaluation indicator is calculated. For the i-th evaluation indicator, its wavelet coefficient S i The formula for calculating the sum is as follows: Traverse the evaluation indicators, if the evaluation indicator X i And the evaluation index X j The wavelet coefficient between is greater than the preset threshold, which means that X i and X j There is multicollinearity between i and X j The wavelet coefficients and the evaluation indicators greater than the preset threshold are removed from the evaluation indicator system, and finally M core evaluation indicators K = {K1,…,K M }; M core evaluation indicators constitute the core evaluation indicator system.

6. A method for evaluating the stability of a secondary suspended river as claimed in claim 1, characterized in that: The specific process of the projection pursuit-TOPSIS comprehensive evaluation model in S3 includes: S31, initialization of projection direction; randomly generate a set of projection direction vectors α=(β1,β m ,…,β M ), where β m is the projection direction coefficient of the mth core evaluation index; S32, calculating the projection value: calculating the projection value of the core evaluation index of the t-th evaluation object according to the projection direction α, where the evaluation object is different river sections, and the specific calculation formula is as follows: in, is the value of the mth core evaluation indicator of the tth evaluation object; S33, optimizing the projection direction based on the established projection value optimization mathematical model, and iteratively optimizing the projection direction α using an evolutionary algorithm to obtain the projection direction α that minimizes the fitness function Fitness * ; S34, construct a weighted decision matrix; * Multiply it with the core evaluation index to obtain the weighted decision matrix V(m,t): S35, select the maximum value of each core indicator in V(m,t) to form a positive ideal solution vector Select the minimum value of each core indicator in V(m,t) to form a negative ideal solution vector S36, calculating the Euclidean distance of each evaluation object to the positive ideal solution and the negative ideal solution; S37, calculating the cosine distance between each evaluation object and the positive ideal solution and the negative ideal solution, the specific calculation formula is as follows: Among them, ∥·∥ is the symbol for calculating the vector modulus, K t is the core evaluation index vector of the tth evaluation object, is the cosine distance between the tth evaluation object and the positive ideal solution, is the cosine distance between the tth evaluation object and the negative ideal solution; S38, calculate the proximity of each evaluation object according to the Euclidean distance and the cosine distance, and the specific calculation formula is as follows: Among them, C t is the proximity of the tth evaluation object, |·| is the absolute value operator; S39, classifying the evaluation objects into stability levels according to the proximity of each evaluation object and a set threshold.

7. A method for evaluating the stability of a secondary suspended river as claimed in claim 6, characterized in that: The established projection value optimization mathematical model is specifically: Construct the following objective function f: f=σ z D z Among them, σ z is the standard deviation of all projection values, D z is the local density of the t-th projection value, and the specific calculation formulas for the two are as follows: Where T is the number of evaluation objects, is the mean of the projection values ​​of all evaluation objects; standard deviation σ z The larger the value is, the higher the dispersion of the projection value in one-dimensional space is, that is, the more obvious the difference in stability between different river sections is; H is the bandwidth of the Gaussian kernel, z ρ For z t The ρth neighborhood element of , γ is the size of the domain element, ‖·‖ is the operator for finding the modulus length; D z The larger the z t The fewer the neighborhood elements in one-dimensional space, the smaller the local density, and z t The more obvious the difference between the stability of the represented river channel and the stability of other river channels; Design the following fitness function Fitness: Where θ is equal to 10 -6 , to ensure that the denominator of the fitness function is not 0.

8. A method for evaluating the stability of a secondary suspended river as claimed in claim 6, characterized in that: In S33, an evolutionary algorithm is used to iteratively optimize the projection direction α, specifically: S331, initialize the population; based on the projection direction α The conditions are as follows: the population size is initialized to N, Population = {P1, P2, ..., P N }, where the nth individual in the population S332, randomly divide Population into two scales Population, one is the constrained population Pop co , and the other is the unconstrained population Pop nco ; S333, Pop co and Pop nco Substitute the population individuals in into the fitness function Fitness to obtain the fitness of each population individual; S334, Pop co and Pop nco Perform binary tournament selection, crossover and mutation operations respectively to obtain the offspring population Off co and Off nco ; S335, set Off co and Off nco Substitute the population individuals in into the fitness function Fitness to obtain the fitness of each population individual; S336, use natural selection operator to update the unconstrained population; set Off co 、Off nco and Pop nco Enter the environment selection operator to obtain the next generation of unconstrained population and replace Pop nco Individuals of the original population; S337, Check Off co and Off nco Do the individuals in the population satisfy If this constraint is not met, the fitness of the individuals in the population that do not meet the constraint will be doubled. S338, use the natural selection operator to update the constrained population; set Off co 、Off nco and Pop co Input the environment selection operator to obtain the next generation of constrained population and replace Pop co Individuals of the original population; S339, determine whether the maximum number of evaluations has been reached. If not, repeat steps S333 to S338 until the maximum number of evaluations is reached and output Pop co ; Pop co The population individual with the smallest fitness is taken as the best projection direction α * .

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