As shown in Figure 3
, the diagnostic process consists of six steps. The diagnosis process is detailed on the left side, including the generation of grayscale co-occurrence matrices, the establishment of standard samples, the training of network models, and the acquisition of diagnostic results. The right side of Figure 3
is the information about the important parameters or results corresponding to the diagnostic steps.
3.2. Triangle Algorithm
The accuracy of extracting feature parameters depends on the optimal generation criteria, including the image gray level, g
, the generative step length, d
, and the generative angle, θ
. Therefore, it is crucial to optimize the factor to obtain accurate and effective feature parameters. Generally, the orthogonal test method (OTM) and full test method (FTM) are used to establish generative criterion. However, OTM leads to the absence of a partial criterion and FTM reduces detection efficiency. Therefore, a new triangulation algorithm used for the confirming of generative criterion is presented in this paper. Figure 5
is the diagram of algorithm.
- Step 1:
The initial range of the factor of the generative criterion is determined according to the properties of the micro-damage image.
- Step 2:
Confirm the generative angle, θ
, by the theory of image rotation invariant. In Figure 5
, the sequence A
is he generative step length, d
is the sequence B
image gray level, g
- Step 3:
The sequence A is linked to the sequence B, and θ is then joined to sequence A and sequence B, respectively.
- Step 4:
Extract all dn-θ-gt combinations. Then, a triangular combination can form.
The algorithm was validated based on the underwater micro-damage diagnosis system. Based on the comparative analysis, the unique advantages of the triangulation algorithm were proven.
In order to ensure the features of the image rotation invariant, the average values directions of 0°, 45°, 90°, and 135° were selected as the generative angle, θ
. Figure 6
is the variations’ form of θ
shows the difference in the characteristic parameters of micro-damage images. The different directions are small. Therefore, the generation angle, θ
, of the generation criterion was determined.
The initial range of the generated standard factor was obtained based on the characteristics of the micro-damage image:
Generative angle, θ: The average of directions of 0°, 45°, 90°, and 135°.
Image gray level: gt = 2m+2, among them, t = m + 2, t is taken as the integer of [1,6].
Generative step length, d: Take the integer of [1,6].
The combination form of the generation standard, dn-θ-gt, was obtained by the triangulation algorithm. It has a total of n × t = n × (m + 2) = 36 groups. The OTM requires determination of the values of the two construction factors in advance to obtain the combined form. If the two construction factors select g and d, the d-θ-g forms a total of 1 × 1 × 4 = 4 groups. Additionally, the FTM does not specify the range of variation of any factor. If the values of d and g are the same as the triangulation algorithm, the d-θ-g forms a total of 6 × 6 × 4 = 144 groups. Experimental verification and comparison results showed that this method can efficiently obtain all the generation criteria of micro damage. The proposed triangulation algorithm obtained the appropriate combination form based on the image properties and effectively improved the detection efficiency.
3.3. Optimization of Generative Criterion
To improve the characteristic performance of structure damage, the generative criterion optimization of GLCM was carried out based on the theory of difference maximization. Figure 7
show the variation tendency of d
, in which the selected characteristic parameters showed a good correlation with the change trend of d. Figure 8
shows the variation form of g
. The selected characteristic parameters are sensitive to the changing trend of g
It can be derived that when d > 4, the characteristic parameter changes tend to be stable basically; when d = 5, the samples of each group can be better distinguished; when d = 6, there is a clear downward trend in aggregation in the correlation, the significant clustering, and the clustering shadow characteristic parameters.
is the variation of g
of six characteristic parameters, including angular second-order moment, entropy maximum probability, etc. It can be analyzed that when g
= 5, each characteristic parameter exhibits high discreteness and high stability.
All the analyses show that the optimal generative criterion, dn-θ-gt, of the underwater structure micro-damage is n is 5, t is 7, and θ is taken as the average of the four directions of 0°, 45°, 90°, and 135°.
3.4. Establishing a Standard Sample Label
For the purpose of obtaining the standard performance parameters of the SOM diagnostic model, the standard sample label was established using the DFS (digital feature screening) method under the optimal generative criteria (d5
, among them, θ
takes 0°, 45°, 90°, and 135°). The DFS method establishes screening criteria for screening parameters by observing the trend of the characteristic parameters of different diagnostic types. The screening criteria are determined according to the size of the intersection interval of different types of damages: The smaller the crossover interval, the better the screening results, and the parameters are suitable for establishing a diagnostic model; otherwise, the parameter is not suitable for diagnosing underwater structural damage. Figure 9
, Figure 10
and Figure 11
shows the screening results.
In Figure 9
, the characteristic parameters occupy their respective intervals with preferable screening results. In Figure 10
, the two types of damage have a small interaction interval, the screening results are ordinary. In Figure 11
, each of the three characteristic parameters is interlaced with each other and each has no independent interval.
The angular second moment, P1
, entropy, P2
, variance of grayscale, P3
, correlation, P4
, inverse matrix, P5
, variance, P6
, significant clustering, P7
, and sums of mean, P8
, were screened. Therefore, the DFS method could effectively solve these problems of characteristic parameter selection. The standard values of each parameter are given in Table 2
gives the standard value of the characteristic parameters corresponding to each kind of damage, which were obtained according to the average value of 200 images.
3.5. Training Network Model
The network model was constructed. The parameters of the network are shown in Table 3
The created network topology is a two-layer network, and the competition layer consists of eight vectors.
. The initial weight was set to 0.125. The neighborhood shape of each network node was set to a hexagon, and the neighborhood radius was set to 3. The competition layer was 8 × 8 = 64 neuron nodes. The training steps were set to 10, 50, 100, 200, 500, and 1000. Table 4
shows the classification effects under different training steps; the numbers in the table represent the classification numbers.
shows that when the number of training steps equals 10, a micro-damage diagnosis model is initially established, and the micro-damage is roughly divided into two groups. With the increase of the number of training steps, when the number of training steps is 50 and 100, respectively, the diagnostic accuracy is further improved. The micro-injury is divided into three groups. When the number of training steps reaches 200, the micro-injury is effectively distinguished. However, when the number of training steps reaches 500 and 1000, the micro-injury classification results are the same as 200 steps, which has no practical significance. Therefore, 200 steps 200 were chosen as the optimal value for the micro-damage diagnosis model.
To verify the reliability of parameter optimization, the topological structure of the winning neurons in Figure 12
was analyzed. The gray hexagon with the number in the figure corresponds to the classification label of the winning neurons.
The unique neighborhood characteristics of SOM and the spatial topology of the input neurons are preserved. Figure 12
shows that the winning neuron numbers are 1, 16, 49, and 64, occupying four different topological spatial locations. The classification result of the topological result graph is completely consistent with the clustering result obtained under the optimal parameters of the network. By analyzing the topology, the network parameters were optimized to build a better SOM network model. It is proven that the setting of various parameters of the network can meet the working requirements of an underwater structure diagnosis system and effectively distinguish the types of micro-damage.
Although the topological position of the winning neurons was obtained, it cannot determine the type of damage for each neuron. Therefore, the neuron distance map was obtained as shown in Figure 13
. Small square hexagons represent neurons and straight lines represent linear connections between neurons. The distance between neurons can be derived from the Euclidean distance formula. The long hexagon of the connected neurons and the depth of the color represents the distance between the neurons.
In Figure 13
, the connected region of the dark hexagon divides the whole neuron into four sub-regions, corresponding to different damage types. The neurons of the light-colored hexagons connected in the sub-area have the same type of damage. Neurons 53 and 60 are surrounded by dark hexagons, corresponding to unknown damage types. Neuron 28 is far from the four types of damage and is classified as micro-voids defects with close proximity. Alternatively, it can be classified as other unknown defects different from 53 and 60 or 28. Therefore, the corresponding situation of all neuronal damage is obtained.
In order to determine the efficiency of the algorithm, test results were analyzed under different test conditions. Table 5
shows the classification of damage.
describes the types of damage that the damage model can identify and the recognition rate for identifying the four types of damage. The data in Table 5
show that the proposed algorithm can not only detect the expected type of defect but also diagnose other unknown defects in the underwater concrete. It can be inferred that when the concrete structure is healthy, Figure 11
will consist of hexagons of a uniform color. Its classification accuracy, R
, can be calculated by the formula:
. While there are only four kinds of damage in the structure, each damage type can be accurately identified. The algorithm can also accurately extract unknown defects. Therefore, the algorithm can obtain good detection results in the case of correct detection, false positive, and false negative detection. It is proved that the algorithm can be applied to the actual detection of underwater structural damage.
3.6. Application and Validation
In order to prove the practicability and reliability of the network parameters and indicators, this method was applied as an example in a measurement project. Figure 14
shows a schematic diagram of the image acquisition system. The micro-damage images obtained are shown in Figure 15
A test sample was constructed as shown in Table 6
. The case of the predicted classification of the sample is shown in Figure 16
This paper used the research methods of comparative analysis and graphs analysis. We can draw the conclusion that each classification predictive sample can correspond to the damage state. All prediction samples were correctly classified and the overall classification accuracy rate was 100%. It showed that the intelligent early warning method achieved satisfactory results and can be used as an intelligent and accurate diagnosis algorithm for solving underwater structural damage under complex constraints.