A gas extraction pipe network leakage fault intelligent detection method

Abstract

The application provides a gas extraction pipe network leakage intelligent detection method, and relates to the technical field of gas extraction, comprising the following steps: drawing a topology graph based on a target pipe network and constructing a gas extraction pipe network working condition solving model; solving and obtaining node flow and negative pressure data under different pipe network leakage conditions by adding gas source nodes at different positions of the extraction pipe network; constructing a two-stage leakage fault diagnosis model from a "leakage pipe section" to a "pipe section leakage point" by using a mathematical model and a BP neural network, and training the neural network model by using pipe network leakage working condition data solved by the above steps; collecting real working condition data of the extraction pipe network, and performing pipe section leakage identification and leakage positioning by using the two-stage leakage fault diagnosis model. The method solves the defect that the leakage point cannot be accurately positioned in the traditional gas extraction pipe network leakage diagnosis technology, replaces the manual inspection method, and saves the cost.

Description

Technical Field

[0001] This invention relates to the field of gas extraction technology, and in particular to an intelligent detection method for gas extraction pipeline network leakage faults. Background Technology

[0002] Gas drainage is the fundamental way to prevent mine gas accidents. Leaks in the gas drainage pipeline network will increase negative pressure loss, reduce the gas drainage concentration, and bring the risk of gas explosion. Therefore, it is of great significance to improve gas drainage efficiency by knowing how to determine whether a gas drainage pipeline network has a leakage fault and how to determine the location and severity of the leak.

[0003] Currently, in intelligent mines, numerous multi-parameter measuring devices with data transmission capabilities are typically installed on the extraction pipelines. These devices enable real-time monitoring of the pipeline network's operating parameters and allow for intelligent adjustment of extraction parameters using control devices. Simultaneously, setting thresholds can provide a basic assessment of pipeline leaks, but this method cannot pinpoint the exact location of the leak.

[0004] Therefore, this invention abstracts the gas extraction pipeline network and combines the advantages of mathematical models and BP neural network methods to establish a two-level leakage fault detection model from "leaking pipe section" to "pipe section leakage point". The intelligent detection method for gas extraction pipeline network leakage faults described in this invention can locate the leakage point, replace manual inspection, reduce costs, and has the advantages of high efficiency and accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide an intelligent detection method for gas extraction pipeline network leakage faults, in order to address the shortcomings of existing technologies, thereby ensuring the normal operation of the gas extraction pipeline network and improving extraction efficiency.

[0006] To achieve the above objectives, this invention provides an intelligent detection method for gas extraction pipeline network leakage faults, specifically including the following steps:

[0007] Step S1: Draw a pipeline topology diagram based on the layout of the target extraction pipeline network system, and construct an extraction pipeline network operating condition solution model based on the pipeline topology and pipe segment characteristic parameters;

[0008] Step S2: Calculate the flow rate and negative pressure data of the gas extraction pipeline network under normal operation using the solution model described in S1; simulate pipeline leakage by adding gas source nodes to the pipeline network topology diagram, and calculate the node flow rate and negative pressure data under different leakage conditions using the extraction pipeline network operating condition solution model.

[0009] Step S3: Construct a two-level leakage fault detection model. The first-level model is a pipe segment leakage identification model, which identifies whether the pipeline network is leaking. If a leak occurs, it outputs the leaking pipe segment number and the level of leakage. The second-level model is a leakage location model, which determines the location of the leak point on the leaking pipe segment. The first-level model is a mathematical model, and the second-level model is a BP neural network model. The training data for the neural network model is the node flow and negative pressure change data obtained in step S2 under different leakage conditions of the pipeline network.

[0010] Step S4: Collect real operating data of the gas extraction pipeline network, and use the secondary leakage fault detection model to identify the leakage situation of the gas extraction pipeline network. If a leakage occurs, output the leakage level and leakage location; otherwise, output that there is no leakage in the pipeline network.

[0011] Furthermore, the pipeline topology diagram in step S1 can be drawn based on the specific mine's mining engineering plan, roadway layout diagram, gas drainage pipeline system diagram, and specific characteristic parameter information of the drainage pipe section.

[0012] Furthermore, the nodes at the connection points between the pipe section and the borehole, the inlet nodes of the extraction pump, and the nodes at the pipe section connections are used as the working condition nodes studied in the working condition solution model and fault diagnosis of the extraction pipeline network.

[0013] Furthermore, the characteristic parameters of the pipeline network include pipe length, pipe diameter, elevation difference, and friction coefficient.

[0014] Furthermore, the construction of the extraction pipeline network operating condition solution model includes establishing corresponding gas state equations, nodal flow conservation equations, mass flow conservation equations, pipeline pressure drop equations, extraction pump characteristic equations, and gas borehole extraction characteristic equations based on the pipeline network topology diagram.

[0015] Step S2 specifically includes the following steps:

[0016] Step S21: Select an appropriate initial source flow rate based on the actual operating data of the target gas extraction pipeline network, and assign the initial source flow rate to the gas extraction pipeline network operating condition solution model to calculate the extraction flow rate and negative pressure data under normal operating conditions;

[0017] Step S22: Add a gas source node to different sections and locations of the gas extraction pipeline in sequence, change the initial flow rate of the node, and use the solution model to calculate the flow rate and negative pressure data of the extraction pipeline node at this time. This will obtain sample data of pipeline operation conditions when different degrees of leakage occur at different locations in the pipeline.

[0018] The first-level model in the secondary fault detection model in step S3 is a mathematical model. By calculating the gas mass flow rate at each node of the pipeline network, the detection model can be used to identify whether a leak has occurred in the pipeline network and the leaking pipe section. Specifically, it includes the following steps:

[0019] S311: Calculate the gas mass flow rate at each node based on the negative pressure, flow rate, temperature and concentration parameters at each node of the pipeline network;

[0020] S312: Using a mathematical model, calculate and compare the gas mass flow rate at the gas inflow and outflow ends of each pipe section in sequence to determine whether a leak has occurred in the pipe section. If a leak has occurred, output the leaking pipe section and the level of leakage, and enter the second-level fault detection model; if no leak has occurred, the fault detection ends directly.

[0021] The second-level model in the secondary fault detection model in step S3 is a BP neural network model. After the leaking pipe segment is output in S312, the model directly enters the neural network model established for that pipe segment to predict the location of the leak. Specifically, it includes the following steps:

[0022] S321: Determine the network structure: Use the negative pressure parameters at each node in the extraction pipeline network as the input part of the neural network, and the output part is the location information of the leak point on the leaking pipe section;

[0023] S322: Data preprocessing: Subtract the normal operating negative pressure data from the leakage operation negative pressure data in S21 from the leakage operation negative pressure data in S22 to obtain the leakage fault negative pressure residual sample matrix. Use the Logistic function to normalize the sample matrix to obtain the normalized leakage fault negative pressure residual sample matrix.

[0024] S323: Establish a neural network model: Establish a leakage fault diagnosis model for each pipe segment: The input layer feature vector is the negative pressure residual sample matrix under the condition that the pipe segment has a leak, and the output layer is the location information of the leak point on the leaking pipe segment.

[0025] S324: Neural Network Training and Parameter Optimization.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] Using monitoring data from the extraction system to identify leaks and faults can truly achieve real-time detection of the extraction system, providing timely updates.

[0028] A large amount of leakage condition sample data was quickly obtained by using mathematical modeling methods. The model was modified according to different mines and different mining periods, which has the advantages of rapid portability and strong practicality.

[0029] The detection process successfully located the leak point with high accuracy. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following figures are used in the description of the embodiments or the prior art:

[0031] Figure 1 This is a schematic diagram of the complete process of an intelligent detection method for gas extraction pipeline network leakage faults.

[0032] Figure 2 This is a schematic diagram of the detection logic for an intelligent detection method for gas extraction pipeline network leakage faults.

[0033] Figure 3 This is a layout diagram of the gas extraction system in an embodiment of the present invention.

[0034] Figure 4 This is a topology diagram of the gas extraction system in an embodiment of the present invention.

[0035] Figure 5 This is a diagnostic effect diagram from an embodiment of the present invention. Detailed Implementation

[0036] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0037] Example 1 and Example 2

[0038] like Figure 1 As shown, this invention applies for an intelligent detection method for gas extraction pipeline network leakage faults, specifically including the following steps:

[0039] Step S1: Draw a pipeline topology diagram based on the layout of the target extraction pipeline system, and construct an extraction pipeline operating condition solution model based on the pipeline topology and pipe segment characteristic parameters.

[0040] Furthermore, the pipeline topology diagram can be drawn based on the specific mine's mining engineering plan, roadway layout diagram, gas drainage pipeline system diagram, and specific characteristic parameter information of the drainage pipe section.

[0041] Furthermore, the pipeline topology diagram includes nodes at the connection points between pipe segments and boreholes (gas source nodes), pipeline segments, nodes at pipe segment connections, auxiliary devices, and nodes at the inlet of the gas extraction pump. Among these, the nodes at the connection points between pipe segments and boreholes, the nodes at the inlet of the extraction pump, and the nodes at pipe segment connections serve as the working condition nodes studied in the operational condition solution model and fault diagnosis of the gas extraction pipeline network.

[0042] Furthermore, the characteristic parameters of the pipeline network include pipe length, pipe diameter, elevation difference, and friction coefficient.

[0043] Furthermore, the resistance coefficient of the pipeline can be calculated using the pressure drop equation of the pipeline section based on the measured negative pressure data of the pipeline network.

[0044]

[0045] Among them, P i and P j λ represents the inlet and outlet pressures of the pipe section, respectively, in Pa; L is the pipe length, in m; λ is the resistance coefficient; M is the gas mass flow rate, in kg / s; Z is the gas compressibility coefficient; R is the gas constant, in kJ / (kg*k); T is the gas temperature, in K; and D is the pipe diameter, in m.

[0046] Furthermore, the construction of the extraction pipeline network operating condition solution model includes establishing corresponding gas state equations, nodal flow conservation equations, mass flow conservation equations, pipeline pressure drop equations, extraction pump characteristic equations, and gas borehole extraction characteristic equations based on the pipeline network topology diagram.

[0047] Furthermore, the characteristic equation for gas borehole extraction is shown below. The parameters in the equation can be obtained by fitting measured data of flow rate and negative pressure at the borehole orifice:

[0048]

[0049] Among them, M i , , These represent the total gas mass flow rate, air mass flow rate, and methane mass flow rate extracted from the i-th borehole, respectively, in kg / s; P i The negative pressure at the orifice of the i-th borehole is Pa; a ai a gi b ai b gi c ai and c gi These are characteristic coefficients.

[0050] Step S2: Calculate the flow rate and negative pressure data of the gas extraction pipeline network under normal operation using the solution model described in S1; simulate pipeline leakage by adding a gas source node to the pipeline network topology diagram, and calculate the node flow rate and negative pressure data under different leakage conditions using the extraction pipeline network operating condition solution model.

[0051] Step S3: Construct a two-level leakage fault detection model. The first-level model is a pipe segment leakage identification model, which first identifies whether the pipeline is leaking. If a leak occurs, it outputs the leaking pipe segment number and the level of leakage. The second-level model is a location model, which determines the location of the leak point on the leaking pipe segment. The first-level model is a mathematical model, and the second-level model is a neural network model. The data required for training the neural network model are the node flow and negative pressure change data under different leakage conditions of the pipeline obtained in step S2.

[0052] Furthermore, the location of the leak point is indicated by the ratio of the length of the leak point to the gas inflow end of the pipe segment to the total length of the pipe segment.

[0053] The first-level model in the secondary fault detection model in step S3 is a mathematical model. By calculating the gas mass flow rate at each node of the pipeline network, the detection model can be used to identify whether a leak has occurred in the pipeline network and the leaking pipe section. Specifically, it includes the following steps:

[0054] S311: Calculate the gas mass flow rate at each node based on the negative pressure, flow rate, temperature, and concentration parameters at each node of the pipeline network.

[0055] S312: Using a mathematical model, calculate and compare the gas mass flow rate at the gas inflow and outflow ends of each pipe section in sequence to determine whether a leak has occurred in the pipe section. If a leak has occurred, output the leaking pipe section and the level of leakage, and enter the second-level fault detection model; if no leak has occurred, the fault detection ends directly.

[0056] Furthermore, the second-level model in the secondary leakage fault detection model in step S3 is a BP neural network model. After the leaking pipe segment is output in S312, the model directly enters the neural network model established for that pipe segment to identify the location of the leak. Specifically, this includes the following steps:

[0057] S321: Determine the network structure: Use the negative pressure parameters at each node in the extraction pipeline network as the input part of the neural network, and the output part is the location information of the leak point on the leaking pipe section.

[0058] S322: Data preprocessing: Subtract the normal operating negative pressure data from the leakage operation negative pressure data in S21 from the leakage operation negative pressure data in S22 to obtain the leakage fault negative pressure residual sample matrix. Use the Logistic function to normalize the sample matrix to obtain the normalized leakage fault negative pressure residual sample matrix.

[0059] S323: Establish a neural network model: Establish a leakage fault diagnosis model for each pipe segment: The input layer feature vector is the leakage residual sample matrix under the condition that the pipe segment has a leakage, and the output layer is the location information of the leakage point on the leaking pipe segment.

[0060] S324: Neural Network Training and Parameter Optimization.

[0061] Furthermore, the number of hidden layer neurons can be determined through trial and error, and particle swarm optimization or genetic algorithm methods can be used for parameter optimization.

[0062] Step S4: Collect real operating data of the gas extraction pipeline network, and use the secondary leakage fault detection model to identify the leakage situation of the gas extraction pipeline network. If a leakage occurs, output the leakage level and leakage location; otherwise, output that there is no leakage in the pipeline network.

[0063] Furthermore, the data collection density for pipeline operation can be once per hour, or the collection density can be adjusted according to the actual conditions of the mine.

[0064] Examples 3 and 4:

[0065] The above-mentioned intelligent detection method for gas drainage pipeline network leakage faults was applied to the drainage pipeline network system of a coal mine. The specific steps are as follows:

[0066] Step L1: Figure 3 The diagram shows the layout of the gas drainage system provided to the mine, which includes three gas source nodes (one high-level oblique drilling site and two in-seam drainage drilling sites). Its pipeline topology is shown below. Figure 4 As shown, there are a total of 7 nodes (3 source nodes, 3 pipe segment sink nodes, and 1 extraction pump inlet node) and 6 pipe segments; based on Figure 4 The established mathematical model for gas drainage operation includes six independent pipeline pressure drop equations, one gas drainage pump characteristic equation, and three independent drainage borehole end characteristic equations, as shown below:

[0067]

[0068] in:

[0069] —Total gas flow rate extracted at node i ;

[0070] —The gas and air flow rate extracted at node i ;

[0071] — Pure gas flow at node i ;

[0072] —Total gas flow rate extracted from pipe section s ;

[0073] —Air flow rate of extracted gas in pipe section s ;

[0074] —Pure gas flow rate of pipe section s. ;

[0075] —Gas concentration in the extracted gas of pipe section s, %;

[0076] —Air flow rate of extracted gas in pipe section s ;

[0077] —Pure gas flow rate of pipe section s. ;

[0078] Z—Gas compressibility coefficient;

[0079] —Gas temperature, K;

[0080] —Node i extracts absolute pressure. ;

[0081] —The relative volume of gas extracted at node i. ;

[0082] —Gas density extracted at node i ;

[0083] — Extraction gas constant, kJ / (kg*k);

[0084] —Gas concentration in the extracted gas at node i, %;

[0085] —Gas constant for air, 0.287 kJ / (kg*k);

[0086] —Gas constant, 0.5182 kJ / (kg*k);

[0087] P atm —Atmospheric pressure, 101325 Pa;

[0088] P 抽 —Absolute pressure at the inlet of the gas extraction pump, Pa. ;

[0089] —i node mixed gas mass flow rate ;

[0090] —Absolute pressure of sampling at the entry point j node ;

[0091] —Absolute pressure of extraction at node k at the export end ;

[0092] — Corrected length of pipe segment s, in meters;

[0093]

[0094] —Standard pipe length of pipe segment s, in meters;

[0095] —Equivalent length of local resistance in pipe segment s, in meters;

[0096] T0 — Gas temperature, K;

[0097] M s —The flow rate of extracted gas within pipe segment s, kg / s;

[0098] R0——The extraction gas constant in pipe segment s, kJ / (kg*k);

[0099] D s —Inner diameter of pipe segment s, in meters;

[0100] sin s θ — the slope of pipe segment s;

[0101] λ s —The resistance coefficient of pipe segment s;

[0102] M ai —Air flow rate at the drilling site end of the pipeline connection, kg / s;

[0103] M gi —Gas extraction volume at the drilling site end of the pipeline section, kg / s.

[0104] Step L2: Calculate the flow rate and negative pressure data of each node when the pipeline network is operating normally using the established extraction pipeline network operating condition solution model; then calculate the operating condition data of the pipeline network under different leakage conditions by adding gas source nodes to each pipe segment and at different locations in the extraction system network topology diagram.

[0105] Furthermore, the ratios of the distance from the new gas source node to the gas inflow end of the pipeline segment to the total length of the pipeline segment are 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 0.99, respectively, and the flow rates of the new gas source nodes are 10%, 15%, 20%, 25%, 30%, 35% and 40% of the total extracted gas.

[0106] The samples were processed using the above method, resulting in 7*10*6=420 sets of leakage samples, with 7*10=70 sets of leakage sample data for each pipe section.

[0107] Step L3: Construct a two-level fault detection model. The first-level model makes a preliminary judgment on whether the pipeline is leaking and the leaking pipe section. The second-level model locates the leak point of the leaking pipe section.

[0108] Furthermore, the first-level model employs a mathematical model to determine whether a pipe segment has leaked by calculating the gas mass flow rate through each node. When a pipe segment leaks, the gas mass flow rate at nodes after the leak point will be greater than the flow rate at nodes before the leak point.

[0109]

[0110] Where, ρ leak The density of the leaked gas is kg / m³. 3 Q leak For the leaked gas flow rate, m 3 / s.

[0111] ρ leak Q leak = η, then we have:

[0112]

[0113] Here, η is the ratio of the leaked gas mass flow rate to the total gas mass flow rate of the pipeline network, reflecting the degree of leakage. In actual extraction processes, pipeline leakage is unavoidable, therefore η > 0. By classifying the values ​​of η, the degree of leakage in the pipeline network can be graded. When a leak occurs in the extraction pipeline network, this leakage identification model can accurately determine the number of the leaking pipe section and the degree of leakage.

[0114] Furthermore, the leakage level of the extraction pipeline system in Example 3 can be divided into four levels: mild (η<0.05), moderate (0.05≤η<0.1), severe (0.1≤η<0.3), and damaged or broken (η≥0.3).

[0115] Furthermore, the second-level model is a BP neural network with 6 neurons in the input layer, 1 neuron in the output layer, and 6 neurons in the hidden layer after multiple trials.

[0116] Furthermore, samples with minimal negative pressure changes are manually removed, ensuring that the remaining samples have negative pressure changes within the sensor's testing accuracy range.

[0117] Finally, the BP neural network completed its learning after 97 iterations. Figure 5 The model predicts the location of the leaking pipe section when the leakage rate is 28%, with a maximum error of 11%, indicating good prediction performance.

Claims

1. A method for intelligent detection of leakage faults in gas extraction pipeline networks, characterized in that, Specifically, the following steps are included: Step S1: Draw a pipeline topology diagram based on the layout of the target extraction pipeline network system, and construct an extraction pipeline network operating condition solution model based on the pipeline topology and pipe segment characteristic parameters; Step S2: Calculate the flow rate and negative pressure data of the gas extraction pipeline network during normal operation using the solution model described in S1; The method of adding gas source nodes to the pipeline network topology diagram is used to simulate pipeline network leakage. The node flow and negative pressure data under different leakage conditions are calculated by using the extraction pipeline network operating condition solution model. Step S3: Based on the leakage condition sample data obtained in Step S2, a two-level leakage fault detection model is constructed. The first-level model is a pipeline leakage identification mathematical model based on the conservation of gas mass flow rate. It is used to calculate the gas mass flow rate at each node of the gas extraction pipeline network according to the negative pressure, flow rate, temperature and concentration parameters. By comparing the mass flow rate at the gas inflow end and the outflow end of each pipeline segment, it identifies whether a leak has occurred in the gas extraction pipeline network and the pipeline segment where the leak has occurred, and outputs the corresponding leaking pipeline segment number and leakage level. The second-level model is a leak location BP neural network model, which only runs in the leaking pipeline segment identified by the first-level model. It is used to locate the specific location of the leak point within the leaking pipeline segment, and the location of the leak point is represented by the continuous position parameters of the leak point relative to the length of the leaking pipeline segment. Step S4: Collect real operation data of the gas extraction pipeline network. Based on the leaking pipe section identified by the first-level model, call the corresponding second-level model to intelligently detect the leakage of the gas extraction pipeline network. When a leak occurs, output the leakage level and the location information of the leak point in the leaking pipe section; otherwise, output that there is no leakage in the gas extraction pipeline network. Step S21: Select an appropriate initial source flow rate based on the actual operating data of the target gas extraction pipeline network, and assign the initial source flow rate to the gas extraction pipeline network operating condition solution model to calculate the extraction flow rate and negative pressure data under normal operating conditions; Step S22: Add a gas source node to different sections and locations of the gas extraction pipeline in sequence, change the initial flow rate of the node, and use the solution model to calculate the flow rate and negative pressure data of the extraction pipeline node at this time. This will obtain sample data of pipeline operation conditions when different degrees of leakage occur at different locations in the pipeline.

2. The intelligent detection method for gas extraction pipeline network leakage faults according to claim 1, characterized in that: The pipeline topology diagram in step S1 is drawn based on the specific mine's mining engineering plan, roadway layout diagram, gas drainage pipeline system diagram, and specific characteristic parameter information of the drainage pipe section. The nodes at the connection end of the pipe section and the borehole, the inlet node of the drainage pump, and the nodes at the connection point of the pipe section are used as the working condition nodes studied in the working condition solution model and fault diagnosis of the drainage pipeline network. The characteristic parameters of the pipeline network include pipe length, pipe diameter, elevation difference, and friction coefficient. The construction of the working condition solution model of the drainage pipeline network includes establishing the corresponding gas state equation, node flow conservation equation, mass flow conservation equation, pipeline pressure drop equation, drainage pump characteristic equation, and gas borehole drainage characteristic equation based on the pipeline topology diagram.

3. The intelligent detection method for gas extraction pipeline network leakage faults according to claim 1, characterized in that: The first-level model in the secondary leakage fault detection model in step S3 is a mathematical model. By calculating the gas mass flow rate at each node of the pipeline network, the detection model can be used to identify whether a leak has occurred in the pipeline network and the leaking pipe section. Specifically, it includes the following steps: S311: Calculate the gas mass flow rate at each node based on the negative pressure, flow rate, temperature and concentration parameters at each node of the pipeline network; S312: Using a mathematical model, calculate and compare the gas mass flow rate at the gas inflow and outflow ends of each pipe section in sequence to determine whether a leak has occurred in the pipe section. If a leak has occurred, output the leaking pipe section and the level of leakage, and enter the second-level fault detection model; if no leak has occurred, the fault detection ends directly.

4. The intelligent detection method for gas extraction pipeline network leakage faults according to claim 1, characterized in that: The second-level model in the secondary leakage fault detection model in step S3 is a BP neural network model. After the leaking pipe segment is output in S312, the model directly enters the neural network model established for that pipe segment to predict the location of the leak. Specifically, it includes the following steps: S321: Determine the network structure: Use the negative pressure parameters at each node in the extraction pipeline network as the input part of the neural network, and the output part is the location information of the leak point on the leaking pipe section; S322: Data preprocessing: Subtract the normal operating negative pressure data from the leakage operation negative pressure data in S21 from the leakage operation negative pressure data in S22 to obtain the leakage fault negative pressure residual sample matrix. Use the Logistic function to normalize the sample matrix to obtain the normalized leakage fault negative pressure residual sample matrix. S323: Establish a neural network model: For each pipe segment, a leakage fault diagnosis model is established, where the input layer feature vector is the negative pressure residual sample matrix under the condition that the pipe segment has a leak, and the output layer is the location information of the leak point on the leaking pipe segment. S324: Neural Network Training and Parameter Optimization.

Images