KR20220090757A - Method and apparatus for estimating position and inpulse of collision with submerged floating tunnel - Google Patents

Abstract

In the method for estimating the impact location and amount of impact of an underwater tunnel according to the present invention, when an impact occurs in the underwater tunnel, a measurement step of measuring impact information through a sensor provided in the underwater tunnel, an artificial neural network-based collision built through data learning and an input step of inputting the impact information into an analysis model and an output step of outputting the impact location and impact amount analyzed by the impact analysis model. The method and apparatus for estimating the impact location and impact amount of an underwater tunnel according to the present invention provides a method for evaluating the impact location and impact amount when a collision with an external approach occurs in relation to the stability of the underwater tunnel. Since the present invention utilizes a pre-learned artificial neural network, it improves reliability even in extreme conditions in the ocean where various variables exist, and can be very usefully used in the design of an underwater tunnel.

Description

Method and apparatus for estimating the impact location and impact amount of an underwater tunnel

The present invention relates to stability evaluation of an underwater tunnel collision, and more particularly, to a method and apparatus for estimating a collision location and an impact amount when an underwater tunnel collides with an external object.

Recently, due to problems such as continuous population growth, resource depletion, and environmental pollution, methods for the continuation and survival of human civilization are being sought. Among them, the submerged floating tunnel is one of the representative civil structures considering the marine environment.

1 is a schematic diagram of an underwater tunnel; The underwater tunnel structure is a collection of various technologies such as structural design technology, construction technology, energy supply technology, movement technology, and safety maintenance technology. .

In relation to the safety maintenance and management of underwater tunnels, the most essential technology is the technology to prevent and predict the collision of external objects such as ships, submarines, and large fish. When a collision occurs in an underwater tunnel, large-scale damage to the structure causes enormous economic damage related to repairs and repairs, as well as human casualties. Therefore, it is necessary to research and develop a technology that can evaluate the safety due to the collision of the underwater tunnel.

There are still not many studies that can evaluate the safety of collisions in underwater tunnels.

Republic of Korea Patent Registration No. 10-1686043 (Title of the invention: Ship collision monitoring system for offshore structures, Applicant: Korea Plant Management Co., Ltd.) is a navigational aid facility that helps the safe operation of ships and loading crude oil or LNG into a ground storage tank To this end, it relates to a ship collision monitoring system of an offshore structure that detects a collision caused by a ship of an offshore structure such as a pier on which a pipeline is erected.

However, in a complex large structure such as an underwater tunnel, not a simple structure such as a pipeline, various variables in the extreme marine environment can be considered only by the general method of comparing the collision index and the critical value as in Korean Patent Registration No. 10-1686043. There is a problem that there is no

Republic of Korea Patent Registration No. 10-1053139 (Title of the invention: Collision prevention structure of an offshore bridge and its construction method, Applicant: Samsung C&T Corporation) is a construction of an offshore bridge with sufficient strength and durability while being easy to construct despite offshore work. It relates to an anti-collision structure and its construction method. Republic of Korea Patent Registration No. 10-1053139 discloses only the configuration of the structure for preventing the collision, there is no disclosure about the technical means for promoting safety.

Republic of Korea Patent Registration No. 10-1686043 (Registration Date: 2016.12.07.) Republic of Korea Patent Registration No. 10-1053139 (Registration Date: 2011.07.26.)

The present invention has been devised in view of the above technical needs, and an object of the present invention is to provide a method for evaluating the safety of a structure in the event of a collision with an external approach by targeting a special structure called an underwater tunnel. In particular, unlike the conventional analysis of physical data from the perspective of structural dynamics and dynamics, a method for estimating the impact location and impact amount of an underwater tunnel that can increase the accuracy even in the presence of various variables more reliably and more reliably by using a pre-learned artificial neural network, and It is an object of the present invention to provide a device.

The present invention is to quantitatively predict the physical damage caused by a collision that may occur in an underwater tunnel. When a collision occurs, acceleration data is acquired through a sensor attached to a structure, and the collision location and amount of impact are identified through the established technique. Specifically, the collision location and the impact amount are obtained by an artificial neural network (ANN)-based algorithm based on the physical quantities measured in the structure. An object of the present invention is to "establish a technique for constructing an algorithm that can determine the location of a collision and the amount of impact of a colliding body".

The method for estimating the impact location and impact amount of an underwater tunnel according to the present invention for achieving the above object is a measurement step of measuring impact information through a sensor provided in the underwater tunnel when an impact occurs in the underwater tunnel, through data learning and an input step of inputting the impact information to the built-up artificial neural network-based collision analysis model and an output step of outputting the collision location and the amount of impact analyzed by the collision analysis model.

In addition, the sensor includes a plurality of unit sensors arranged to have a predetermined separation distance in the underwater tunnel, and the plurality of unit sensors may measure acceleration, speed, and displacement information due to a collision.

In addition, the collision analysis model may include: an input layer for receiving learning data including acceleration data for each span; a hidden layer including a plurality of nodes for calculating the acceleration data for each span; and an output layer for outputting the impact location and impact amount filtered by the hidden layer.

And, the determination step of determining the safety level of the underwater tunnel based on the collision position and the amount of impact output in the output step; may further include.

In addition, the safety level may be set by comparing the amount of impact output in the output step with a preset threshold value.

On the other hand, the apparatus for estimating the collision position and impact amount of the underwater tunnel according to the present invention for achieving the above object includes a plurality of sensors arranged with a predetermined separation distance outside the underwater tunnel; a collision analysis unit that analyzes the impact information measured by the plurality of sensors using a collision analysis model based only on artificial nerves; and a result value output unit for outputting the collision location and the amount of impact analyzed by the collision analysis unit.

In addition, the sensor may measure acceleration, velocity, and displacement information due to a collision with the underwater tunnel.

In addition, the collision analysis model may include: an input layer for receiving learning data including acceleration data for each span; a hidden layer including a plurality of nodes for calculating the acceleration data for each span; and an output layer for outputting the impact location and impact amount filtered by the hidden layer.

It may further include; a safety level determination unit for determining the safety level of the underwater tunnel based on the collision position and the amount of impact output from the result output unit.

In addition, the safety level may be determined by comparing the amount of impact output from the result value output unit with a preset threshold value.

The method and apparatus for estimating the impact location and impact amount of an underwater tunnel according to the present invention provides a method for evaluating the impact location and impact amount when a collision with an external approach occurs in relation to the stability of the underwater tunnel. Since the present invention utilizes a pre-learned artificial neural network, it improves reliability even in extreme conditions in the ocean where various variables exist, and can be very usefully used in the design of an underwater tunnel.

The present invention is different from the prior art related to collision in that it is made for a special structure called an underwater tunnel, and the prior art only analyzes the collision from the point of view of structural dynamics and dynamics of the physical data generated by the collision. However, in the present invention, reliability can be improved because the collision location and the amount of impact are identified by using a pre-learned artificial neural network.

1 is a schematic diagram of an underwater tunnel;
2 is a schematic diagram for explaining a collision location and impact amount estimation method of an underwater tunnel according to the present invention.
3 is a flowchart of a method for estimating the impact location and impact amount of an underwater tunnel according to the present invention.
4A to 4C illustrate a concept of identifying a collision location and an impact amount using an artificial neural network-based collision analysis model.
5 is a view for explaining a process of securing learning data for constructing an artificial neural network-based collision analysis model.
6 shows a layer structure of an artificial neural network-based collision analysis model according to the present invention.
7 shows a collision analysis model constructed for a method for estimating a collision location and an impact amount of an underwater tunnel according to the present invention.
8A to 8C are graphs showing the learning results of the collision analysis model used in the present invention.
9A and 9B are results of verifying the collision analysis model using learning data and non-learning data.
10 is a view for explaining a method of determining a critical impact amount and setting a safety level through collision analysis construction.
11 is a block diagram illustrating a configuration of an apparatus for estimating a collision location and an impact amount of an underwater tunnel according to the present invention.

Hereinafter, the embodiments disclosed in the present specification will be described in detail with reference to the accompanying drawings, but the same or similar components are assigned the same reference numbers regardless of reference numerals, and redundant description thereof will be omitted. The suffix "part" for the components used in the following description is given or mixed in consideration of only the ease of writing the specification, and does not have a meaning or role distinct from each other by itself. In addition, in describing the embodiments disclosed in the present specification, if it is determined that detailed descriptions of related known technologies may obscure the gist of the embodiments disclosed in the present specification, the detailed description thereof will be omitted. In addition, the accompanying drawings are only for easy understanding of the embodiments disclosed in the present specification, and the technical idea disclosed herein is not limited by the accompanying drawings, and all changes included in the spirit and scope of the present invention , should be understood to include equivalents or substitutes.

2 is a schematic diagram for explaining a collision location and impact amount estimation method of an underwater tunnel according to the present invention. As shown in FIG. 2 , the underwater tunnel is a longitudinal structure installed in the water, and various devices such as rails and trains are included in the inside blocked from the outside (undersea). Underwater tunnels have a risk of collision with external access objects, for example, creatures or submarines passing through the seabed.

Therefore, it is necessary to completely block external collisions for the operation of the submarine tunnel, but since it is impossible to block 100% of this, an environment that can predict the possibility of collision with an external approach and prepare in advance must be prepared.

As shown in FIG. 2, a plurality of sensors (Sensor1, Sensor2, Sensor3, Sensor4, Sensor...) arranged at preset intervals are disposed in the underwater tunnel. When an external approach approaches the underwater tunnel, water waves are transmitted to each sensor, and the physical quantity detected by each sensor is different. In addition, since the time at which the waves strike is different, the temporal change of a physical quantity may also have a specific pattern.

Figure 2 (a) is a diagram modeling an underwater tunnel to obtain algorithm learning data using an analysis model, Figure 2 (b) is the data (Data1, Data2, Data3, Data4, Data5 ...) from each sensor After obtaining , the collision location and the amount of impact are estimated based on this, and the process of determining the safety level of the underwater tunnel based on the impact is shown. That is, the safety is evaluated by comparing it with the standard threshold value through the estimated impact amount and the collision analysis result. The safety level of the underwater tunnel can be classified into five of safety (Step 1), concern (Step 2), caution (Step 3), warning (Step 4), and danger (Step 5), but in other embodiments, various modifications can be

3 is a flowchart of a method for estimating the impact location and impact amount of an underwater tunnel according to the present invention.

First, when an impact occurs in the underwater tunnel, impact information is measured through a sensor provided in the underwater tunnel (S110). This becomes the basis for data learning and becomes the input information of the built artificial intelligence model. Step S110 is made by a plurality of sensors disposed in the underwater tunnel. The sensor includes a plurality of unit sensors arranged to have a predetermined separation distance in the underwater tunnel, and the plurality of unit sensors may measure acceleration, velocity, and displacement information due to a collision.

If data learning has already been performed, the impact information measured in step S110 is input to the collision analysis model (S120). A plurality of sensors inputs impact information to a CPU (Central Process Unit), GPU (Graphic Processing Unit), controller, etc. that perform crash analysis, and the CPU or controller analyzes the input impact information based on the crash analysis model.

Finally, the collision location and impact amount analyzed by the collision analysis model are output (S130). The output impact location and impact amount may be used to determine the safety level. That is, after the output step (S130), a determination step of determining the safety level of the underwater tunnel by a CPU or a controller may be further included.

Here, the collision analysis model secures learning data (acceleration, displacement information, etc. due to collision) through numerical analysis, and is built with an artificial neural network-based algorithm through data learning. That is, the acceleration and/or displacement data for each point measured by the sensor is used as input data for an algorithm to determine the collision location and the amount of impact. This will be described in more detail below.

4A to 4C illustrate a concept of identifying a collision location and an impact amount using an artificial neural network-based collision analysis model.

The collision analysis model is built based on artificial neural networks. Learning data for using artificial neural networks can be obtained by using a commercial numerical analysis program.

Here, we built training data for an artificial neural network (ANN)-based collision analysis model using SAP 2000. That is, the analysis target marine structure (underwater tunnel) shown in FIG. 4A is modeled as shown in FIG. 4B. Then, when the force of the impact amount F is applied to the impact location (Point 86) shown in FIG. 4A , the impact load according to the time history is analyzed as shown in FIG. 4C . In FIG. 4C , the horizontal axis indicates time, and the vertical axis indicates the amount of impact.

After modeling the offshore structure in the order of FIGS. 4A to 4C , a collision numerical analysis is performed while applying various input loads, and a collision analysis model is constructed by learning it.

5 is a view for explaining a process of securing learning data for constructing an ANN-based collision analysis model.

First, using SAP 2000, an offshore structure is modeled as shown in the left drawing of FIG. 5 . Thereafter, when the collision load occurs, the change in the magnitude of the acceleration with time is observed for each point of each span. The magnitude of the acceleration response at each point may be different, and the closer the point to the collision, the higher the acceleration value is observed. The acceleration response at the center of each span is shown in the graph on the right of FIG. 5 . Here, the horizontal axis means time, and the vertical axis means an acceleration value.

It inputs and trains acceleration response data according to various collision cases. That is, the impact amount of the impact body is calculated by learning the input values and result values related to the impact location, the physical quantity of the impact body, and the arrival time of the impact. That is, the acceleration data obtained through numerical analysis is used as learning data for the algorithm.

6 shows a layer structure of an artificial neural network-based collision analysis model according to the present invention.

The collision analysis model according to the present invention may be divided into an input layer, a hidden layer, and an output layer. First, the input layer receives the acceleration data for each span measured by the sensor, more specifically, the acceleration data obtained through the numerical analysis described in FIG. 5 . In addition to the acceleration data, the physical quantity data of the colliding body may be further input.

The hidden layer performs calculations and analysis while changing the collision location and impact amount. The hidden layer includes a plurality of nodes that repeatedly learn the acceleration response at the collision location. Finally, in the output layer, new input data (data of a new condition not used for learning) is input, and the result value (collision position and impact amount) filtered in the hidden layer is output.

The analyzed (estimated) results (impact location and impact amount) are used for safety evaluation. Based on the safety evaluation result, an appropriate response scenario can be configured and used for underwater tunnel design.

7 shows a collision analysis model constructed for a method for estimating the collision location and impact amount of an underwater tunnel according to the present invention, and FIGS. 8A to 8C are graphs showing the learning results of the collision analysis model used in the present invention.

The collision analysis model constructed for the method for estimating the impact location and impact amount of an underwater tunnel according to the present invention numerically analyzed the spring-supported 10-span beam structure in SAP2000, and constructed learning data by changing the impact load position. The learning data may be an acceleration value, a physical quantity of a colliding body, an arrival time, and the like.

After building the training data, use Neural Network Toolbox in MATLAB to build an artificial neural network that can estimate the collision location and impact amount. Here, the input data is the maximum value and arrival time measured by 10 accelerometers (total of 20 input nodes), and the output data is whether or not there is a collision in 5 spans (total of 5 output nodes).

As shown in FIG. 7 , the details of the algorithm are as follows.

Data Division: Random (dividerand)

Training: Scaled Conjugate Gradient (Trainscg)

Performance: Cross-Entropy (crossentropy)

Calculations: MEX

9A and 9B are results of verifying a collision analysis model using learning data and non-learning data.

Validation of the collision analysis model was performed using learning and non-learning data. 9A is a performance verification result using data used for learning, and FIG. 9B is a performance verification result using data not used for learning. 9A and 9B , the horizontal axis indicates the position of the sensor, and the vertical axis indicates the amount of impact.

As shown in FIGS. 9A and 9B , the collision location and the amount of impact could be accurately estimated by any of the data used for learning and the data not used for learning.

10 is a view for explaining a method of determining a critical impact amount and setting a safety level through the construction of a collision analysis model. The collision location and impact amount estimated using the collision analysis model built through the learning data becomes the basis for safety evaluation.

That is, if the amount of impact is grasped by the collision analysis model as shown in the left graph of FIG. 10 , it is classified based on the threshold value. Here, the threshold value is a value obtained by performing collision and fracture analysis, and sets the stage at which structural problems may occur due to collision. In FIG. 10, a total of five steps are classified, but may be set differently according to embodiments.

The present invention relates to a technique for determining the location of a collision and an amount of impact by using an artificial neural network-based algorithm constructed for safety evaluation of a structure when an underwater tunnel collides with an external approach, and the following effects can be achieved.

(1) Based on the analysis technique using artificial neural networks, it is possible to estimate the impact location and impact amount simply and quickly without complicated calculations.

(2) In the event of a collision, the structural safety of offshore structures can be identified early and effectively.

(3) The safety of users using the structure can be secured.

11 is a block diagram showing the configuration of the apparatus 100 for estimating the impact location and impact amount of an underwater tunnel according to the present invention. As shown in FIG. 11 , the apparatus 100 for estimating the collision location and the amount of impact of the underwater tunnel according to the present invention includes a sensor 110 , a collision analysis unit 120 , a result value output unit 130 and a safety level determination unit ( 140).

The sensors 110 are arranged at predetermined intervals in the underwater tunnel. As shown in FIG. 2, each of the unit sensors (Sensor1, Sensor2, Sensor3, Sensor4, Sensor...) may be disposed at the same or different intervals, but is preferably disposed at regular intervals. When an external approach approaches the underwater tunnel, water waves are transmitted to each sensor, and the physical quantity detected by each sensor is different. In addition, since the time at which the waves strike is different, the temporal change of a physical quantity may also have a specific pattern. The sensor 110 measures acceleration, velocity, and displacement information due to a collision with the underwater tunnel.

The collision analyzer 120 and the result output unit 130 may be included in the same configuration. That is, the names of the collision analysis unit 120 and the result output unit 130 only refer to components that are functionally classified differently, and do not need to be physically distinct individual components. It is sufficient that the collision analysis unit 120 and the result output unit 130 are modules capable of performing calculations, such as a CPU or a controller.

The collision analysis unit 120 receives impact information measured by a plurality of sensors and analyzes it using an artificial neural network-based collision analysis model. The collision analysis model is learned based on the acquired learning data, and the output data is derived by calculating the input data input from the sensor.

The collision analysis model is built based on an artificial neural network, and the learning data for using the artificial neural network can be obtained by using a commercial numerical analysis program. It performs modeling of offshore structures, performs collision numerical analysis while applying various input loads, and builds a collision analysis model by learning it.

Specifically, when a collision load occurs, the change in the magnitude of the acceleration with time is observed for each point of each span. The magnitude of the acceleration response at each point may be different, and the closer the point to the collision, the higher the acceleration value is observed. It inputs and trains acceleration response data according to various collision cases. That is, the impact amount of the impact body is calculated by learning the input values and result values related to the impact location, the physical quantity of the impact body, and the arrival time of the impact. That is, the acceleration data obtained through numerical analysis is used as learning data for the algorithm.

The collision analysis model may be divided into an input layer, a hidden layer, and an output layer. First, the input layer receives the acceleration data for each span measured by the sensor, more specifically, the acceleration data obtained through the numerical analysis described in FIG. 5 . In addition to the acceleration data, the physical quantity data of the colliding body may be further input. The hidden layer performs calculations and analysis while changing the collision location and impact amount. The hidden layer includes a plurality of nodes that repeatedly learn the acceleration response at the collision location. Finally, in the output layer, new input data (data of a new condition not used for learning) is input, and the result value (collision position and impact amount) filtered in the hidden layer is output. The analyzed (estimated) results (impact location and impact amount) are used for safety evaluation. Based on the safety evaluation result, an appropriate response scenario can be configured and used for underwater tunnel design.

The result output unit 130 outputs the collision position and the amount of impact from the collision analysis unit 120 . As mentioned above, the function of the result output unit 130 may be included in the collision analysis unit 120 .

The safety level determination unit 140 determines the safety level of the underwater tunnel based on the collision location and the amount of impact output from the result value output unit 130 . The safety level may be determined by comparing the amount of impact output from the result value output unit with a preset threshold value. The function of the safety level determination unit 140 may also be included in the collision analysis unit 120 . That is, the collision analysis unit 120 , the result output unit 130 , and the safety level determination unit 140 may be implemented as an integral configuration (eg, CPU).

In relation to artificial neural network learning, when performing inter-layer calculation of an artificial neural network, the calculation may be performed by multiplying input data input to a node of the corresponding layer by a predetermined associated parameter (or weight, w). Then, after summing (weighted sum) of all the calculation results performed at each node (usually matrix multiplication or convolution product is usually used), it passes through a preset activation function to generate predetermined output data and move to the next layer. transmit Activation functions are a step function, a sign function, a linear function, a logistic sigmoid function, a hyper tangent function, a ReLU function, and a softmax ( softmax) function can be used, but is not limited thereto. Usually used. The activation function is appropriately selected when designing the structure of the artificial neural network model suitable for the application field. Learning of artificial neural networks is machine learning in which all relevant parameters (w) in the neural network are repeatedly updated (or modified) to appropriate values. Machine learning of an artificial neural network may be performed by selecting one of supervised learning, unsupervised learning, and reinforcement learning. In addition, the method for estimating the impact location and impact amount of an underwater tunnel according to the present invention may use a deep learning algorithm having a plurality of hidden layers for data clustering and classification.

On the other hand, the method for estimating the impact location and impact amount of the underwater tunnel according to the present invention described above may be implemented in the form of a program command that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable recording medium may include program instructions, data files, data structures, etc. alone or in combination. The program instructions recorded on the medium may be specially designed and configured for the present invention, or may be known and available to those skilled in the art of computer software. Examples of the computer-readable recording medium include magnetic media such as hard disks, floppy disks and magnetic tapes, optical media such as CD-ROMs and DVDs, and magnetic such as floppy disks. - includes magneto-optical media, and hardware devices specially configured to store and execute program instructions, such as ROM, RAM, flash memory, and the like. Examples of program instructions include not only machine language codes such as those generated by a compiler, but also high-level language codes that can be executed by a computer using an interpreter or the like. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the present invention, and vice versa.

Features, structures, effects, etc. described in the above embodiments are included in one embodiment of the present invention, and are not necessarily limited to one embodiment. Furthermore, features, structures, effects, etc. illustrated in each embodiment can be combined or modified for other embodiments by those of ordinary skill in the art to which the embodiments belong. Accordingly, the contents related to such combinations and modifications should be interpreted as being included in the scope of the present invention.

100: device for estimating the impact location and impact amount of the underwater tunnel
110: sensor
120: collision analysis unit
130: result output unit
140: safety level determination unit

Claims (10)

In the method for estimating the impact location and impact amount of the underwater tunnel,
a measuring step of measuring impact information through a sensor provided in the underwater tunnel when an impact occurs in the underwater tunnel;
an input step of inputting the impact information into an artificial neural network-based collision analysis model built through data learning; and
An output step of outputting the impact location and impact amount analyzed by the impact analysis model; Containing, Method for estimating impact location and impact amount of an underwater tunnel. According to claim 1,
The sensor includes a plurality of unit sensors arranged to have a predetermined separation distance in the underwater tunnel, wherein the plurality of unit sensors measure acceleration, velocity, and displacement information due to a collision, estimating the impact location and impact amount of the underwater tunnel Way. According to claim 1,
The collision analysis model is,
an input layer receiving learning data including acceleration data for each span;
a hidden layer including a plurality of nodes for calculating the acceleration data for each span; and
An output layer for outputting the impact location and impact amount filtered from the hidden layer; Containing, a method for estimating impact location and impact amount of an underwater tunnel. According to claim 1,
A determination step of determining a safety level of the underwater tunnel based on the impact location and impact amount output in the output step; further comprising, a method for estimating impact location and impact amount of the underwater tunnel. 5. The method of claim 4,
The safety level is set by comparing the amount of impact output in the output step with a preset threshold value, the collision location and impact amount estimation method of the underwater tunnel. A plurality of sensors arranged with a predetermined separation distance outside the underwater tunnel;
a collision analysis unit that analyzes the impact information measured by the plurality of sensors using an artificial neural network-based collision analysis model; and
Containing, apparatus for estimating the impact location and impact amount of the underwater tunnel; including; 7. The method of claim 6,
The sensor measures acceleration, velocity, and displacement information due to the collision with respect to the underwater tunnel, the collision location and impact amount estimation device of the underwater tunnel. 7. The method of claim 6,
The collision analysis model is,
an input layer receiving learning data including acceleration data for each span;
a hidden layer including a plurality of nodes for calculating the acceleration data for each span; and
An output layer for outputting the impact location and impact amount filtered from the hidden layer; Containing, the apparatus for estimating impact location and impact amount of the underwater tunnel. 7. The method of claim 6,
A safety level determination unit for setting a safety level of the underwater tunnel based on the collision position and the amount of impact output from the result output unit; further comprising, an apparatus for estimating the impact location and impact amount of the underwater tunnel. 10. The method of claim 9,
The safety level is determined by comparing the amount of impact output from the result value output unit with a preset threshold value, the collision location and impact amount estimation apparatus of the underwater tunnel.

Images