CN108629364B - Identification method of non-Gaussian seabed landform types based on multifractal spectral features - Google Patents

Identification method of non-Gaussian seabed landform types based on multifractal spectral features Download PDF

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CN108629364B
CN108629364B CN201810197919.2A CN201810197919A CN108629364B CN 108629364 B CN108629364 B CN 108629364B CN 201810197919 A CN201810197919 A CN 201810197919A CN 108629364 B CN108629364 B CN 108629364B
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王微微
王大伟
吴时国
吴一琼
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China University of Petroleum East China
Institute of Deep Sea Science and Engineering of CAS
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Abstract

本发明公开了一种基于多重分形谱特征的非高斯型海底地貌类型识别方法。包括如下步骤：1)根据海底深度测量数据计算深度分布偏度和峰度，判断地形是否为非高斯型地形；2)计算非高斯型地形的多重分形谱特征；3)将多重分形谱特征作为原始变量，应用因子分析方法提取地貌因子；4)根据地貌因子，应用支持向量机设计地貌类型分类器；5)计算待识别地貌的地形深度分布偏度和峰度，判断地形的非高斯性，计算非高斯型地形的多重分形谱特征及其地貌因子，应用设计的分类器识别地貌类型。本发明具有方法简单、计算量小、识别准确率高、节约人力等优点。本发明适用于非高斯型海底地貌类型识别。

Figure 201810197919

The invention discloses a non-Gaussian seabed landform type identification method based on multi-fractal spectral features. It includes the following steps: 1) calculating the skewness and kurtosis of the depth distribution according to the seabed depth measurement data, and judging whether the terrain is a non-Gaussian terrain; 2) calculating the multifractal spectral features of the non-Gaussian terrain; 3) using the multifractal spectral features as For the original variables, the factor analysis method is used to extract the landform factors; 4) According to the landform factors, the support vector machine is used to design the landform type classifier; The multifractal spectral features and their geomorphic factors of non-Gaussian terrain are calculated, and the designed classifier is used to identify the terrain types. The invention has the advantages of simple method, small calculation amount, high recognition accuracy, labor saving and the like. The invention is suitable for identification of non-Gaussian seabed landform types.

Figure 201810197919

Description

non-Gaussian submarine landform type identification method based on multi-fractal spectral features
Technical Field
The invention relates to the technical fields of ocean mapping, ocean engineering, ocean oil and gas resources and the like, in particular to a non-Gaussian submarine landform type identification method based on multi-fractal spectrum characteristics.
Background
Topography is the general term for various relief forms on the earth's surface. Types of submarine topography include ancient watercourses, scour troughs, submarine canyons, deep water channels, sea mountains, carbonate terraces, scarps, landslides, and the like. The landform classification is the basis of submarine landform research and drawing, and the landform form can reflect the internal relation between the landform cause type and the cause control form, and is the key for deep-layer geological knowledge mining.
The multi-beam sounding system can detect the submarine topography and landform fine characteristics with wide coverage and high resolution. The system adopts strip type measurement, can simultaneously measure the water depth value of dozens or even hundreds of seabed measured points in a plane vertical to the direction of the flight line or a full-coverage water depth strip with a certain width, and can accurately and quickly measure the size, the shape and the height change of an underwater target in a certain width along the flight line.
The landform parameters are digital descriptions of landforms and are used for characterizing the spatial distribution of the landforms. Geomorphic parameters are numerous and vary in understanding and categorizing them in different disciplines and areas. In the current research, the geomorphic parameters mainly relate to two major categories, namely microscopic parameters and macroscopic parameters. The microscopic parameters describe and reflect topographical features of a particular location. The commonly used microscopic parameters mainly include gradient, slope direction, slope length, plane curvature, section curvature, etc. The macroscopic parameters describe and reflect topographical features over a large area. Common macro parameters mainly comprise terrain depth standard deviation, terrain difference entropy, terrain roughness, elevation variation coefficient and the like.
At the end of the 20 th century, Mandelbrot, a French mathematician, proposed a concept of fractal to represent complex processes or graphs. Fractal is a general term for self-similar patterns and structures with certain meaning but without characteristic length. Fractal structures are widely found in nature, and for example, coastlines, snowflakes, trees, clouds, and the like all have fractal structures. Multi-fractal is a measure of a two-or three-dimensional object that has spatial self-similarity or statistical self-similarity. The multi-fractal structure has non-Gaussian property, and the multi-fractal spectrum can reflect the complexity of the object structure.
The submarine landforms are complex, at present, the recognition of submarine landform types is limited, a large amount of landform type analysis is mainly completed manually, and the submarine landform types are distinguished and identified through observation and experience of technicians. The method can fully utilize knowledge of technicians, has good flexibility, but needs the technicians to have rich geoscience knowledge and observation and judgment experience, has great subjectivity, and has the defects of poor timeliness, high labor intensity and the like. Particularly, because the submarine data has a mass level, the processing task of the mass data cannot be born by the manual capability of technicians.
Disclosure of Invention
The method determines whether the terrain depth distribution has non-Gaussian property according to the kurtosis and skewness of the submarine terrain, extracts the space structure characteristics of fractal spectrum features representing the terrain of the non-Gaussian terrain, extracts the landform factors reflecting the landform types by applying a factor analysis method, and establishes a landform type classifier through a support vector machine to realize landform type identification. The extracted multi-fractal spectrum characteristics comprise multi-fractal spectrum width, multi-fractal spectrum peak value, maximum and minimum fractal dimension difference, capacity dimension and correlation dimension. The method has the advantages of simplicity, small calculated amount, high identification accuracy, manpower saving and the like. The method is suitable for identifying the type of the non-Gaussian submarine landform.
The invention comprises the following steps:
(1) judging non-Gaussian terrain:
are respectively based on
Figure GDA0002888531590000021
Calculating the skewness m of the seabed depth of the area to be identified1Kurtosis m2If m is satisfied1> 0 and m2If the terrain is more than 0, the terrain of the area to be identified is non-Gaussian type terrain, wherein ziFor the normalized depth value of the sea floor at the ith measuring point in the area to be identified,
Figure GDA0002888531590000022
the average value of the depth of the sea bottom is obtained, and n is the number of measurement points in the area to be identified;
(2) calculating the characteristics of the multi-fractal spectrum:
according to respective Δ α ═ αmax-αmin、f(α(q))max＝max(f(α(q)))、Δf＝f(αmax)-f(αmin) And DqCalculating fractal spectrum width Δ α, fractal spectrum peak f (α (q))maxMaximum and minimum fractal dimension difference delta f and dimension DqWherein, when q is 0, DqFor capacity dimension, q is 2 hours DqFor the correlation dimension, max (f (α (q))) represents taking the maximum value of f (α (q)), α (q) being the Hausdor dimension of the topographic depth distribution of the area to be identified, αmaxIs the maximum singularity index, alphaminF (alpha (q)) is a distribution density function, alphamax、αminAlpha (q) and f (alpha (q)) are obtained by calculation by using a Chhabra algorithm, wherein q is a scale parameter and is set in the Chhabra algorithm;
(3) extracting landform factors based on multi-fractal spectrum characteristics:
original variables are Δ α, f (α (q))maxΔ f and DqExtracting a common factor f of the original variables by using a factor analysis methodiI is 1,2,3, … …, the variance contribution ratio of each factor is λiI is 1,2,3, … …, if satisfied
Figure GDA0002888531590000023
F is theniI is 1,2, … …, and is a landform factor based on the multi-fractal spectrum characteristics, wherein t is the number of common factors, fi、λiT is determined according to factor analysis, theta is a threshold value and is set in program parameters, and j is the number of topographic factors;
(4) and (3) designing a landform type classifier:
according to the landform factor f i1,2, … …, applying a support vector machine to determine a landform type classifier;
(5) and (3) landform type identification:
calculating the skewness and kurtosis value m of the terrain depth of the landform to be identified1And m2If m is satisfied1> 0 and m2If the number is more than 0, calculating the multi-fractal spectrum characteristics of the landform to be identified and the landform factor value f thereofiAnd (5) determining the type of the landform to be identified according to the classifier obtained in the step (4), wherein i is 1,2 and … ….
Drawings
Fig. 1(a) to 1(e) are topographical views of 5 types of terraces, including a seabed terrace, a gully, a landslide, a ridge, and a water course, respectively;
FIG. 2 is a cross-sectional view of skewness and kurtosis of the depth distribution of 5 kinds of landforms;
FIGS. 3(a) to 3(f) are cross-sectional views of fractal spectral features of non-Gaussian landforms in this embodiment;
FIG. 4 is a plot of the variance contribution of 5 common factors for 5 multifractal spectral features of a non-Gaussian landform type;
FIG. 5 is a plot of the cumulative variance contribution of 5 common factors for 5 multifractal spectral features of a non-Gaussian landform type;
FIG. 6 is a non-Gaussian landform type classifier in accordance with the present embodiment;
fig. 7 shows the recognition result of the non-gaussian landform type in this embodiment.
Detailed Description
According to the embodiment, according to multi-beam seabed sounding data, the kurtosis and skewness values of seabed terrain are calculated to determine whether the terrain depth distribution has non-Gaussian nature, the multi-fractal spectrum features and the landform factors of the non-Gaussian terrain are extracted, and a landform type classifier is established through a support vector machine to realize the identification of 3 non-Gaussian landform types such as seabed gully, landslide and water channel. The extracted multi-fractal spectrum characteristics comprise multi-fractal spectrum width, multi-fractal spectrum peak value, maximum and minimum fractal dimension difference, capacity dimension and correlation dimension.
The specific identification steps are as follows:
(1) judging non-Gaussian terrain:
are respectively based on
Figure GDA0002888531590000031
Calculating the skewness m of the seabed depth of the area to be identified1Kurtosis m2If m is satisfied1> 0 and m2If the terrain is more than 0, the terrain of the area to be identified is non-Gaussian type terrain, wherein ziFor the normalized depth value of the sea floor at the ith measuring point in the area to be identified,
Figure GDA0002888531590000041
the average value of the depth of the sea bottom is obtained, and n is the number of measurement points in the area to be identified.
In the present embodiment, the seafloor depth data is measured by a multi-beam method, and fig. 1(a) to 1(e) are topographic maps of 5 types of seafloor plateaus, gullies, landslides, ridges, and channels, respectively.
FIG. 2 is the intersection of skewness and kurtosis of the depth distribution of 5 kinds of landforms. The skewness of the depth distribution of the 5 landforms in the embodiment is larger than zero, the kurtosis of all terrace landforms and raised landforms is smaller than zero, the kurtosis of all gully landforms is larger than zero, and the kurtosis of a part of landslides and water channel landforms is larger than zero. Therefore, neither the terrace nor the raised relief in this embodiment has non-gaussian properties; all gullies, a part of landslides and water channel landforms have non-Gaussian properties, and multi-fractal spectrum characteristic values of the gullies and the landslides can be extracted.
(2) Calculating the characteristics of the multi-fractal spectrum:
according to respective Δ α ═ αmax-αmin、f(α(q))max＝max(f(α(q)))、Δf＝f(αmax)-f(αmin) And DqCalculating fractal spectrum width Δ α, fractal spectrum peak f (α (q))maxMaximum and minimum fractal dimension difference delta f and dimension DqWherein, when q is 0, DqFor capacity dimension, q is 2 hours DqFor the correlation dimension, max (f (α (q))) represents taking the maximum value of f (α (q)), α (q) being the Hausdor dimension of the topographic depth distribution of the area to be identified, αmaxIs the maximum singularity index, alphaminF (alpha (q)) is a distribution density function, alphamax、αminAlpha (q) and f (alpha (q)) are calculated by using a Chhabra algorithm, and q is a scale parameter and is set in the Chhabra algorithm.
Fig. 3 is a cross-sectional view of the multi-fractal spectral features of a non-gaussian landform in this embodiment. The related multi-fractal spectrum characteristics comprise multi-fractal spectrum width, multi-fractal spectrum peak value, maximum and minimum fractal dimension difference, capacity dimension and correlation dimension.
(3) Extracting landform factors based on multi-fractal spectrum characteristics:
original variables are Δ α, f (α (q))maxΔ f and DqExtracting a common factor f of the original variables by using a factor analysis methodiI is 1,2,3, … …, the variance contribution ratio of each factor is λiI is 1,2,3, … …, if satisfied
Figure GDA0002888531590000042
F is theniI is 1,2, … … is a landform factor based on the characteristic of multi-fractal spectrum, wherein t is the number of common factors, f isi、λiT is determined by factor analysis, theta is a threshold value set in the program parameters, and j is the number of topographic factors.
In this embodiment, the number of common factors of the original variables of the non-gaussian landform is t ═ 5, fig. 4 shows the variance contribution rate distribution of 5 common factors of the 5 multi-fractal spectral features of the non-gaussian landform type, and fig. 5 shows the cumulative variance contribution rate of 5 common factors of the 5 multi-fractal spectral features of the non-gaussian landform type. In this example, θ is 50%, and 2 topographic factors are obtained.
(4) And (3) designing a landform type classifier:
according to the landform factor fiAnd i is 1,2 and … …, and a support vector machine is applied to determine the landform type classifier.
In the present embodiment, 2 geomorphic factors are extracted, and fig. 6 shows a non-gaussian geomorphic type classifier in the present embodiment.
(5) And (3) landform type identification:
calculating the skewness and kurtosis value m of the terrain depth of the landform to be identified1And m2If m is satisfied1> 0 and m2If the number is more than 0, calculating the multi-fractal spectrum characteristics of the landform to be identified and the landform factor value f thereofiAnd (5) determining the type of the landform to be identified according to the classifier obtained in the step (4), wherein i is 1,2 and … ….
FIG. 7 is a diagram illustrating the recognition result of non-Gaussian landform types in this embodiment.

Claims (1)

1.一种基于多重分形谱特征的非高斯型海底地貌类型识别方法，其特征包括如下具体步骤：1. a non-Gaussian seabed landform type identification method based on multifractal spectrum feature, its feature comprises the following concrete steps: (1)非高斯型地形判断：(1) Non-Gaussian terrain judgment: 分别根据
Figure FDA0002888531580000011
计算待识别区域的海底深度的偏度m1、峰度m2，如果满足m1＞0且m2＞0，则待识别区域地形为非高斯型地形，其中，zi为待识别区域内第i个测量点处的归一化后的海底深度值，
Figure FDA0002888531580000012
为海底深度平均值，n为待识别区域内测量点数；respectively according to
Figure FDA0002888531580000011
Calculate the skewness m 1 and kurtosis m 2 of the seabed depth of the area to be identified. If m 1 >0 and m 2 >0 are satisfied, the terrain of the area to be identified is non-Gaussian terrain, where zi is the area within the area to be identified. the normalized seabed depth value at the i-th measurement point,
Figure FDA0002888531580000012
is the average value of seabed depth, and n is the number of measurement points in the area to be identified; (2)多重分形谱特征计算：(2) Multifractal spectrum feature calculation: 分别根据
Figure FDA0002888531580000013
f(α(q))max＝max(f(α(q)))、Δf＝f(αmax)-f(αmin)和Dq＝α(q)*q-f(α(q))/(1-q)计算多重分形谱宽Δα、多重分形谱峰值f(α(q))max、最大最小分形维数差Δf、维数Dq，其中，q＝0时Dq为容量维数，q＝2时Dq为关联维数，max(f(α(q)))表示取f(α(q))的最大值，α(q)为待识别区域地形深度分布的Hausdor维数，αmax为最大奇异性指数，αmin为最小奇异性指数，f(α(q))为分布密度函数，αmax、αmin、α(q)和f(α(q))应用Chhabra算法计算得到，q为尺度参数，在Chhabra算法中设定；respectively according to
Figure FDA0002888531580000013
f(α(q)) max = max(f(α(q))), Δf = f(α max )-f(α min ) and D q =α(q)*qf(α(q))/ (1-q) Calculate the multifractal spectrum width Δα, the multifractal spectrum peak value f(α(q)) max , the maximum and minimum fractal dimension difference Δf, and the dimension D q , where D q is the capacity dimension when q=0 , when q=2, D q is the correlation dimension, max(f(α(q))) means taking the maximum value of f(α(q)), and α(q) is the Hausdor dimension of the topographic depth distribution of the area to be identified , α max is the maximum singularity index, α min is the minimum singularity index, f(α(q)) is the distribution density function, α max , α min , α(q) and f(α(q)) use the Chhabra algorithm Calculated, q is the scale parameter, which is set in the Chhabra algorithm; (3)基于多重分形谱特征的地貌因子提取：(3) Geomorphic factor extraction based on multifractal spectral features: 原始变量为Δα、f(α(q))max、Δf和Dq，应用因子分析方法提取原始变量的公共因子fi，i＝1,2,3,……,t，各因子的方差贡献率为λi，i＝1,2,3,……,t，若满足
Figure FDA0002888531580000014
则fi，i＝1,2,……,j为基于多重分形谱特征的地貌因子，其中，t为公共因子数，fi、λi、t根据因子分析确定，θ为阈值，在程序参数中设定，j为地貌因子数；The original variables are Δα, f(α(q)) max , Δf and D q , and the factor analysis method is used to extract the common factors f i of the original variables, i=1,2,3,...,t, the variance contribution of each factor The rate is λ i , i=1, 2, 3, ..., t, if it satisfies
Figure FDA0002888531580000014
Then f i , i=1,2,...,j are the topographic factors based on multifractal spectral features, where t is the number of common factors, f i , λ i , t are determined according to factor analysis, θ is the threshold, in the program Set in the parameters, j is the number of landform factors; (4)地貌类型分类器设计：(4) The design of the landform type classifier: 根据地貌因子fi，i＝1,2,……,j，应用支持向量机确定地貌类型分类器；According to the landform factors f i , i=1,2,...,j, the support vector machine is used to determine the landform type classifier; (5)地貌类型识别：(5) Identification of landform types: 计算待识别地貌的地形深度的偏度和峰度值m1和m2，若满足m1＞0且m2＞0，则计算待识别地貌的多重分形谱特征及其地貌因子值fi，i＝1,2,……,j，根据步骤(4)得到的分类器确定待识别地貌的类型。Calculate the skewness and kurtosis values m 1 and m 2 of the topographic depth of the landform to be identified. If m 1 >0 and m 2 >0 are satisfied, then calculate the multifractal spectral characteristics of the landform to be identified and its landform factor value f i , i=1,2,...,j, the type of landform to be identified is determined according to the classifier obtained in step (4).
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