Distributed control system topological structure optimization method and system oriented to gas turbine

Abstract

The invention discloses a distributed control system topological structure optimization method and system oriented to a gas turbine, and belongs to the technical field of gas turbine control. The method comprises the following steps: establishing a double-feature grid coding system fusing space coordinates and an adjacent distance matrix, and updating a shortest path between nodes by using a Floyd algorithm; designing a function-resource allocation scheme by combining engineering constraints such as node working temperature limitation and bus load uniformity; the position of a central intelligent node of the star topology structure is optimized by adopting a particle swarm algorithm, and the local wire harness length is shortened; the node connection sequence of the annular topological structure is optimized through a genetic algorithm, and the redundancy of key nodes is improved; and finally, a hybrid topological structure is formed. The example verifies that the total wire harness length of a certain type of gas turbine control system is reduced by 61.6% compared with that of a traditional centralized architecture, the signal transmission reliability is remarkably improved, the development and maintenance cost is reduced, and the method has important engineering application value.

Description

Technical Field

[0001] The present invention belongs to the field of gas turbine control technology, and specifically relates to a distributed control system topology optimization method and system, which is suitable for the design of gas turbine intelligent control architecture. Background Art

[0002] Gas turbines, due to their wide power range, long lifespan, and high reliability, have been widely used in ship propulsion and power generation. With the rapid development of Full Authority Digital Engine Controls (FADECs), gas turbines are becoming fully equipped with digital electronic control systems. However, with increasing performance demands, such as the application of advanced model-based control methods and complex control strategies, traditional centralized digital electronic control technology is increasingly unable to meet the control system requirements of future gas turbines. To address these issues, many experts and scholars have proposed replacing the existing centralized control architecture with a distributed control architecture. The flexibility and scalability of distributed control architectures are reflected not only in the flexible deployment of intelligent nodes and low maintenance costs, but also in the complex and diverse topology design challenges of intelligent node location determination and functional trade-offs. Notably, international manufacturers have pioneered the engineering application of distributed control technology for industrial gas turbines, with GE's MARKVI system being a typical example. In contrast, China is still in the pre-research stage of key technologies in this field and lacks independent and controllable solutions.

[0003] Many heuristic optimization methods have been proposed for gas turbine distributed control system topology optimization both domestically and internationally. However, these algorithm-driven optimization methods suffer from the inherent flaw of improperly allocating intelligent node functions, resulting in insufficient system robustness and limited engineering applicability. Furthermore, most of these optimization methods focus on aircraft engines. Non-aerospace gas turbines differ from aircraft engines in terms of aerodynamic design criteria, thermodynamic environmental constraints, and lifecycle maintenance requirements. Directly applying mature aviation technology systems will lead to significant technical compatibility issues. Therefore, to further develop a theoretical framework for gas turbine-oriented distributed control system architecture design, research on gas turbine intelligent distributed control system architecture design methods has important theoretical significance and engineering application value.

[0004] The present invention forms a complete design paradigm including spatial modeling-topology optimization through the deep integration of hybrid optimization strategies at the algorithm level and engineering constraints, providing a solution for the design of gas turbine distributed control architecture that is both theoretically innovative and engineering feasible. Summary of the Invention

[0005] The technical problem addressed by this invention is to overcome the shortcomings of existing technologies. Based on the urgent needs of precise grid modeling of the complex, variable-radius geometric features of gas turbines, balanced allocation of intelligent node functions and resources, and global optimization of communication network topology, a distributed control system topology optimization method is provided, which can be used to design the architecture of an intelligent distributed control system for gas turbines. Using a certain type of gas turbine as a validation target, the proposed method, while considering engineering constraints such as node temperature tolerance and multimodal signal transmission, yielded an intelligent distributed topology solution that reduced the total control system wiring length by 61.6% compared to traditional centralized architectures. This approach effectively improves signal transmission reliability and reduces development and maintenance costs.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for optimizing a distributed control system topology for a gas turbine includes the following steps:

[0008] Step A. Establishing a grid coding system with dual features of spatial coordinates and distance matrix to represent nodes on the gas turbine;

[0009] Furthermore, step A includes:

[0010] a. Establish a mesh model containing the geometric features of the gas turbine for the object;

[0011] b. Take a cross-sectional circle for every unit length along the axial direction. Each cross-sectional circle is divided into 100 equal parts. Take a grid point on the first cross-sectional circle as the starting point and number them clockwise with natural numbers. The number of each grid point can reflect the axial position of the cross-sectional circle where the point is located and the circumferential position within the cross-sectional circle, that is, the spatial coordinates.

[0012] c. Record the distance information from each grid point to the surrounding points to generate an undirected adjacency matrix, and use graph theory and Floyd's shortest path algorithm to update the distance between any two grid points;

[0013] d. Use a grid numbering system to represent the topological relationships between all central intelligent nodes and slave accessories of the gas turbine.

[0014] In step c, the Floyd shortest path algorithm tests whether any path lengths have changed by enumerating each slack point. As slack points are added sequentially, each pair of points in the graph is traversed to determine whether the minimum distance between them has changed due to the addition of the slack point. If so, the distance between the two points is updated with the shorter value.

[0015] Step B. Design node function-resource allocation scheme considering key engineering constraints;

[0016] The design of the solution described in Step B should consider key engineering constraints that affect system stability and development and maintenance costs in actual projects, including node operating temperature limits, bus load uniformity, node spatial layout, different control loops, different modal signals, and different sensor types. This solution can be flexibly adjusted according to the application scenario.

[0017] Step C. Based on the node function-resource allocation scheme, the particle swarm algorithm is combined to optimize the positions of the central intelligent nodes of all star topologies to ensure the shortest wire harness length of all star topologies.

[0018] Furthermore, step C includes:

[0019] a. Combine all node grid numbers and gas turbine geometry to divide each node position into z i ,θ i , r i The three parts represent the axial position, circumferential position, and radial position of the i-th central intelligent node. Assuming that there are n central intelligent nodes in the gas turbine, the position and velocity of all particles in the particle swarm are encoded as

[0020] x=[z1,θ1,r1…z i ,θ i ,r i …,z n ,θ n ,r n ]

[0021]

[0022] b. Take the length of the connecting harness as the optimization object and select the objective function f as:

[0023]

[0024] Where η is the number of star topology structures, d k represents the set of connection bundle lengths from the central intelligent node k to its slave nodes. The bundle length value is taken from the adjacency matrix, and min(·) represents the minimum value in the set;

[0025] c. Optimize the central intelligent node location that satisfies the shortest connection harness for each star topology structure.

[0026] Step D: Based on the existing central intelligent node positions, the connection sequence of the central intelligent nodes of the ring topology structure is optimized in combination with the genetic algorithm to ensure that the wiring harness length of the ring topology structure is the shortest and the connection redundancy of the key nodes is higher;

[0027] Furthermore, step D includes:

[0028] a. Selection and encoding of chromosome individuals. Here, chromosome individuals are set as the connection sequence between central intelligent nodes, with different numbers corresponding to different node connection schemes. Selecting n nodes and numbering them from 1 to n transforms the wiring problem of the communication bus between central intelligent nodes into a 1 to n sorting problem. In other words, the encoding of the individuals is a random ordering of natural numbers from 1 to n. This encoding method minimizes coding complexity while also accounting for redundancy constraints on the connections of important nodes.

[0029] b. Establishment of objective function and calculation of fitness

[0030] Suppose a chromosome individual

[0031] pop=(N1,N2,…,Nn)

[0032] Where: Ni (i=1~n) corresponds to the grid number of node i.

[0033] Assume that the nodes with connection redundancy of 2 are Na and Nb. Then the objective function f is

[0034]

[0035] Where d(·) represents the shortest link distance between a pair of nodes, which is obtained from the adjacency matrix.

[0036] c. Combine crossover and mutation operations to optimize the central intelligent node connection sequence that satisfies the shortest connection harness of the global ring topology.

[0037] Step E: Combining the two optimization results to form an optimal gas turbine hybrid topology design scheme.

[0038] The present invention also provides a gas turbine distributed control system based on the method, comprising:

[0039] Temperature-resistant deployment module: The central intelligent node has a built-in microprocessor, with an operating temperature of ≤80°C, and uses linear interpolation mapping to avoid deployment in high-temperature areas of the fuselage;

[0040] Central intelligent node cluster: deployed at the gas turbine base, including temperature sensor nodes, speed sensor nodes, data concentrators, and independent control loop nodes. Each node number is mapped to the grid coding system.

[0041] Communication bus network: It is composed of a hybrid structure combining star topology and ring topology, where:

[0042] A star topology connects the central intelligent node with the slave accessories, and the bundle length is based on the shortest path in the adjacency matrix;

[0043] Ring topology connects the communication links between central intelligent nodes, and dual-line redundancy is set up for key nodes;

[0044] Data is exchanged between the online chip detection device, the health management computer, the digital electronic control cabinet and the upper monitoring unit through independent communication channels.

[0045] The present invention also provides an application of the method in a ship power gas turbine control system, comprising:

[0046] Aiming at the variable radius geometric characteristics of ship gas turbines, a dual-feature grid coding system is constructed, with an axial section division density of 100 equal divisions per unit length, to achieve accurate characterization of the central intelligent node and the position of the slave accessories;

[0047] Establish a mapping relationship between the gas turbine body and the base, and deploy the central intelligent node on the gas turbine base to meet its operating temperature limit requirements;

[0048] The particle swarm algorithm is used to optimize the position of the central intelligent node in the star topology, and the genetic algorithm is used to optimize the connection method of the central intelligent node in the ring topology. The hybrid topology structure reduces the wiring harness length by 61.6% compared with the original optimization.

[0049] Independently set up a star topology of high-bandwidth nodes including upper-level monitoring units and online chip detection devices to meet the independence and high-bandwidth requirements of corresponding communication circuits;

[0050] Multi-loop communication links are set up in the ring topology to meet the multi-redundancy of communication loops and key nodes, and improve the fault tolerance of the control system.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] This paper addresses the design of gas turbine distributed control architectures and develops a complete design paradigm encompassing spatial modeling and topology optimization. Specifically, a hybrid topology optimization method for the communication network of a gas turbine distributed control system based on a multi-layer intelligent algorithm is proposed to address the distributed control topology optimization problem. Results show that:

[0053] 1) The grid coding system constructed by the present invention, which has the dual characteristics of spatial coordinates and distance matrix, can accurately represent the topological relationship of nodes in multi-stage variable-diameter gas turbines;

[0054] 2) This invention proposes a node function partitioning solution to address the node function-resource matching problem, while flexibly expanding the central intelligent node location solution strategy to minimize changes to the existing system;

[0055] 3) The present invention proposes a highly redundant structure design scheme with multiple loops of a ring bus and multiple connections of important nodes to meet the high reliability requirements of the control system;

[0056] 4) The optimization method proposed in the present invention can generate an optimal hybrid topology structure that combines a local star topology with a global ring topology, which can shorten the control harness length of a certain type of gas turbine by 61.6%. A shorter harness length means less signal attenuation and interference, which can effectively improve signal transmission reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a schematic diagram of the topology optimization method of the distributed control system for gas turbines according to the present invention.

[0058] Figure 2 This is a structural diagram of a certain type of gas turbine.

[0059] Figure 3 This is a schematic diagram of the temperature distribution of a certain type of gas turbine fuselage.

[0060] Figure 4 This is the overall architecture diagram of the gas turbine intelligent distributed control system.

[0061] Figure 5 It is a two-dimensional plane connection diagram of the temperature sensor central intelligent node 1.

[0062] Figure 6 It is a two-dimensional plane connection diagram of the temperature sensor central intelligent node 2.

[0063] Figure 7 It is a two-dimensional plane connection diagram of the data concentrator.

[0064] Figure 8 It is a two-dimensional plane connection diagram of the central intelligent node of the ejector position controller.

[0065] Figure 9 It is a ring topology diagram.

[0066] Figure 10 It is the iteration graph of the wire harness length of the ring topology.

[0067] Figure 11 It is a hybrid topology diagram. DETAILED DESCRIPTION

[0068] The technical solution of the present invention is described in detail below with reference to the accompanying drawings:

[0069] Figure 1This is a schematic diagram of the distributed control system topology optimization method for gas turbines according to the present invention. From a macro perspective, the topology optimization process can be divided into five steps. Step 1 is to establish a dual-feature grid coding system for the object and represent all nodes with grid numbers. Step 2 is node function-resource allocation, which determines the slave nodes included in the local star topology formed by each central intelligent node. Step 3 is the particle swarm algorithm optimization process for the star topology, which determines the positions of each central intelligent node. Step 4 is the genetic algorithm optimization process for the ring topology, which determines the optimal connection order of the central intelligent nodes. Step 5 is to combine the above optimization processes to determine the optimal gas turbine hybrid topology.

[0070] Figure 2 This is a structural diagram of a gas turbine. Some accessory information is shown in Tables 1 and 2. A grid coding system is used to generate the corresponding accessory node numbers. In traditional centralized gas turbine control architectures, the installation location of slave accessory nodes is not limited to the turbine body. To ensure control signal integrity, the slave accessory nodes on the turbine side and in the control room are considered to be deployed on the base. Subsequently, research was conducted to optimize the communication bus topology for both the gas turbine body and base based on the slave accessory installation location.

[0071] Table 1 Gas turbine fuselage accessory information

[0072]

[0073] Table 2 Gas turbine base accessory information

[0074]

[0075] While existing communication network topologies optimized using heuristic algorithms can minimize wire length within layout constraints, they fail to effectively address key engineering constraints that impact system stability and development and maintenance costs, including node operating temperature limits and bus load uniformity. To overcome the inherent engineering limitations of algorithm-driven node function allocation, this paper investigates the functional partitioning of central intelligent nodes for gas turbine distributed control systems, addressing the challenge of function-resource matching under multiple constraints.

[0076] Consider the average temperature distribution of each section of the gas turbine fuselage as follows Figure 3As shown. The temperature resistance of the central intelligent node of the communication bus is mainly limited by the microprocessor and other components built into the node. At present, the maximum operating temperature of the central intelligent node under the military-grade standard can exceed 100°C, but it still cannot meet the requirements of being directly deployed on the gas turbine body. Since the base temperature is about 80°C under normal working conditions, the design of the present invention deploys the central intelligent node on the base to meet the node operating temperature requirements. Since the deployment position of the gas turbine slave accessories is not unique, in order to reduce the design and maintenance costs, the slave accessories on the gas turbine body and the corresponding central intelligent node installed on the base are connected in the shortest possible wiring method. The central intelligent node location strategies for each star topology structure are solved as shown in Table 3.

[0077] Table 3 Central intelligent node location solution strategy

[0078]

[0079] Most slave accessories in the gas turbine control system transmit very small amounts of data or only transmit a small amount of switching or analog signals with a period of 25ms, which can be ignored here. The relevant information of slave accessories with large amounts of data is shown in Table 4:

[0080] Table 4 Data transfer from accessories

[0081]

[0082] Based on the hierarchical design principle of the system architecture, the attachments listed in Tables 1 and 2 are classified as follows: (1) The digital electronic control cabinet should be divided into independent central intelligent nodes due to its system-level control properties; (2) According to Table 4, the upper monitoring unit, the chip online monitoring device data processing unit and the health management computer are set as independent nodes because they have independent data interaction channels and high transmission bandwidth requirements; (3) The closed-loop control system components (including actuator controllers such as electric starters, electric fuel pumps, and electric actuators) are set as nodes according to the independence of the control loop; (4) The spatially adjacent temperature sensor groups (gas turbine inlet total temperature / lubricating oil temperature, casing temperature / power turbine outlet total temperature) are connected to dedicated temperature processing nodes respectively; the key speed sensors that are far apart are set as independent nodes based on the importance of the signal; the vibration signal conditioner and the pressure transmitter are connected to the corresponding signal type node respectively; (5) The switching devices (air switching valves, etc.) are connected to the bus after protocol conversion through the data concentrator.

[0083] In summary, the overall architecture of the gas turbine intelligent distributed control system is finally formed as follows: Figure 4 shown.

[0084] against Figure 2A simulation experiment of the gas turbine shown in FIG5 is carried out, and is divided into two steps: optimizing the position of the central intelligent node of each local star topology structure and the connection sequence of the central intelligent node of the global ring topology structure.

[0085] Simulation Step 1: Star Topology Optimization Process

[0086] Take some central intelligent nodes as an example:

[0087] 1) Temperature sensor central intelligent node 1

[0088] The total temperature sensor at the gas turbine inlet and the lubricating oil temperature sensor are connected as slaves of the temperature sensor central intelligent node 1. The grid number of the temperature sensor central intelligent node 1 obtained by particle swarm algorithm optimization is 16175 on the fuselage, which is mapped to the corresponding deployment position 6544 on the base through linear interpolation. The corresponding two-dimensional plane connection diagram is as follows Figure 5 shown.

[0089] 2) Temperature sensor central intelligent node 2

[0090] The casing temperature sensor and the power turbine outlet total temperature sensor are connected as slaves of the temperature sensor central intelligent node 2. The grid number of the temperature sensor central intelligent node 2 obtained by particle swarm algorithm optimization is 32350 on the fuselage, and the corresponding deployment position on the base is 22725 through linear interpolation. The corresponding two-dimensional plane connection diagram is as follows Figure 6 shown.

[0091] 3) Data Concentrator

[0092] The air conversion valve, metal end alarm, and igniter power supply are connected as slave accessories of the data concentrator. Since the air conversion valve is deployed on the fuselage and the metal end alarm and igniter power supply are deployed on the base, the air conversion valve is projected from the accessories to the base as the node deployment position and then connected to the metal end alarm. The corresponding central intelligent node deployment position on the base is 7965. The two-dimensional plane connection diagram is as follows Figure 7 shown.

[0093] 4) Ejector position controller central intelligent node

[0094] The ejection position feedback sensor and the reversing solenoid valve are connected as slaves of the central intelligent node of the ejection position controller. Since the ejection position feedback sensor is deployed on the fuselage and the reversing solenoid valve is deployed on the base, the ejection position feedback sensor is projected on the base as the node deployment position and then connected to the reversing solenoid valve. The corresponding central intelligent node deployment position on the base is 23722, and the corresponding two-dimensional plane connection diagram is as follows Figure 8 shown.

[0095] After optimization, the location information of all central intelligent nodes deployed on the base is shown in Table 5.

[0096] Table 5 Central intelligent node location information

[0097]

[0098]

[0099] Simulation Step 2: Ring Topology Optimization Process

[0100] The ring topology is optimized using a genetic algorithm based on the existing central intelligent node locations. The speed sensor central intelligent node 1 and the speed sensor central intelligent node 2 are considered important nodes, and their connection redundancy is set to 2 to improve the system's fault tolerance. At the same time, considering the two independent communication lines between the chip online detection device and the health management computer, and between the upper monitoring unit and the digital electronic controller, the ring topology is finally optimized as follows: Figure 9 As shown in the figure. N3 and N7 are both dual-line redundant, which ensures that when a ring loop fails, the important central intelligent nodes N3 and N7 can still achieve normal node interaction through the other loop. In addition, the two independent communication lines N12-N13 and N14-N15 are temporarily not added to the global ring topology. The iteration of the wire harness length of the ring topology is shown in the figure. Figure 10 shown.

[0101] Combining the above optimization results, the hybrid topology of the gas turbine distributed control system on the base can be obtained as follows: Figure 11 As shown. Ignoring the health management computer, upper monitoring unit, digital electronic control cabinet and corresponding central intelligent node connections that are far away from the gas turbine base, the final total wiring harness length of the gas turbine distributed control system is approximately 4879.9 (dimensionless), while the total wiring harness length of the corresponding traditional centralized control system is approximately 12715.8 (dimensionless). By comparison, it can be seen that the gas turbine control system can save about 61.6% of the wiring harness length by transforming from a centralized architecture to a distributed architecture. Shorter wiring harness length means less signal attenuation and interference, which can effectively improve signal transmission reliability. At the same time, compared with the traditional centralized architecture, the distributed control architecture can significantly improve the computing efficiency and responsiveness of the system, providing support for the application of gas turbine control systems in high-dynamic and high-precision scenarios.

[0102] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for optimizing the topology of a distributed control system for a gas turbine, characterized in that: The following steps are involved: Step A: Establish a grid coding system with dual features of spatial coordinates and distance matrix to represent the nodes on the gas turbine; Step B: Design a node function-resource allocation scheme based on node operating temperature limits, bus load uniformity, and multi-modal signal transmission constraints; Step C: Based on the allocation scheme in step B, the particle swarm algorithm is used to optimize the position of the central intelligent node of the star topology structure, and the objective function is to minimize the total length of the star topology harness; Step D: Based on the optimization results of step C, a genetic algorithm is used to optimize the node connection order of the ring topology structure. The objective function is to minimize the total length of the ring topology harness and improve the redundancy of key nodes. Step E: Combining the optimization results of steps C and D, a hybrid topology design scheme combining star and ring is formed.

2. The method according to claim 1, characterized in that The step A comprises: A1. Build a mesh model that includes the gas turbine's geometric features. A2. Take a cross-sectional circle of every unit length along the axial direction and divide it into 100 equal parts. Number the grid points by natural numbers according to their axial and circumferential positions. A3. Record the distances between grid points to generate an undirected adjacency matrix. Use the Floyd shortest path algorithm to update the shortest path between any two points. A4. The topological relationship between the gas turbine central intelligent node and its accessories is represented by grid numbers.

3. The method according to claim 2, characterized in that Floyd's shortest path algorithm tests whether any path length has changed by enumerating each slack point; when adding slack points sequentially, it needs to traverse every pair of points in the graph to determine whether the minimum distance between each pair of points has changed due to the addition of the slack point. If so, the distance between the two points is updated with the shorter value.

4. The method according to claim 1, wherein The specific implementation of step C includes: C1. Encode the central intelligent node position into three parameters: axial, circumferential, and radial, and iteratively optimize it using a particle swarm algorithm. C2. The objective function is defined as the minimum sum of the bundle lengths in each star topology, where the bundle lengths are taken from the adjacency matrix.

5. The method according to claim 1, wherein The specific implementation of step D includes: D1. Encode the ring topology connection sequence into chromosome individuals arranged in natural numbers; D2. The objective function is defined as the weighted sum of the total length of the ring topology harness and the redundancy of key nodes. Redundancy is achieved by setting up dual nodes. D3. Optimize the global optimal connection order through crossover and mutation operations.

6. The method according to claim 1, characterized in that In step E, the total length of the wiring harness of the hybrid topology structure needs to be compared with the data before and after optimization to verify that the wiring harness length is reduced by 61.6%.

7. A gas turbine distributed control system based on the method according to any one of claims 1 to 6, characterized in that: include: Temperature-resistant deployment module: The central intelligent node has a built-in microprocessor, with an operating temperature of ≤80°C, and uses linear interpolation mapping to avoid deployment in high-temperature areas of the fuselage; Central intelligent node cluster: deployed at the gas turbine base, including temperature sensor nodes, speed sensor nodes, data concentrators, and independent control loop nodes. Each node number is mapped to the grid coding system. Communication bus network: It is composed of a hybrid structure combining star topology and ring topology, where: A star topology connects the central intelligent node with the slave accessories, and the bundle length is based on the shortest path in the adjacency matrix; Ring topology connects the communication links between central intelligent nodes, and dual-line redundancy is set up for key nodes; Data is exchanged between the online chip detection device, the health management computer, the digital electronic control cabinet and the upper monitoring unit through independent communication channels.

8. Application of the method according to claims 1 to 6 in a ship power gas turbine control system, characterized in that: include: Aiming at the variable radius geometric characteristics of ship gas turbines, a dual-feature grid coding system is constructed, with an axial section division density of 100 equal divisions per unit length, to achieve accurate characterization of the central intelligent node and the position of the slave accessories; Establish a mapping relationship between the gas turbine body and the base, and deploy the central intelligent node on the gas turbine base to meet its operating temperature limit requirements; The particle swarm algorithm is used to optimize the position of the central intelligent node in the star topology, and the genetic algorithm is used to optimize the connection method of the central intelligent node in the ring topology. The hybrid topology structure reduces the wiring harness length by 61.6% compared with the original optimization. Independently set up a star topology of high-bandwidth nodes including upper-level monitoring units and online chip detection devices to ensure the independence of corresponding communication circuits and high bandwidth requirements; Multi-loop communication links are set up in the ring topology to meet the multi-redundancy of communication loops and key nodes, and improve the fault tolerance of the control system.

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