A wind power tower drum tower foundation load online monitoring system and method

Abstract

The application provides a wind power tower drum tower base load online monitoring system and method, and relates to the technical field of wind power generation, and comprises a tower base foundation ring strain sensing array for continuously sensing the axial strain of each point in the foundation ring range; a tower base foot bolt strain sensing array for measuring the axial strain of the foot bolt; a distributed optical fiber strain demodulator for synchronously demodulating the axial strain values and temperature values of each point along the optical fiber; an optical fiber grating demodulator for demodulating the strain values of each strain sensor; a calculation collector for data synchronous collection, packaging and uploading; a monitoring server for obtaining the final overturning moment amplitude and direction parameters; and a calculation real-time vertical load resultant force. The application can linearly and completely sense the stretching and compression areas, solves the signal saturation and failure problems caused by the interface separation when measuring the pressure in the contact surface in the prior art, ensures that the system can still work normally under the overturning moment working condition, and realizes direct, online and real-time monitoring.

Description

Technical Field

[0001] This invention relates to the field of wind power generation technology, and in particular to an online monitoring system and method for wind turbine tower foundation load. Background Technology

[0002] With the continued growth in global demand for renewable energy, wind turbines are developing towards larger sizes and taller towers. Currently, the capacity of a single onshore wind turbine has generally reached over 6MW, with rotor diameters exceeding 200 meters and hub heights reaching 140 meters or even higher. These large, high-tower turbines have relatively low safety margins in their design, and structural failures can result in significant downtime losses. Therefore, online monitoring of the structural safety of wind turbines, especially the tower foundation which is the ultimate load-bearer of the entire turbine, has significant engineering value and economic benefits.

[0003] The tower foundation is the core structure that transfers all the loads of the wind turbine (including its own weight, wind load, and operating load) to the ground. The types of loads borne by the tower foundation are complex, mainly including: vertical loads (vertical components caused by the wind turbine's own weight and wind load), overturning moments (bending moments caused by wind load and yaw), and torque. Among these, the magnitude and direction of the overturning moment are the two most critical parameters for assessing the safety status of the tower foundation. Excessive overturning moments can lead to serious accidents such as anchor bolt breakage and separation of the foundation ring from the concrete. Furthermore, uneven settlement or stiffness degradation of the foundation can cause the tower foundation to bear eccentric loads; if this early problem is not detected in time, it will gradually evolve into a catastrophic failure.

[0004] Currently, monitoring technologies for wind turbine towers and foundations can be mainly categorized as follows: (1) Indirect monitoring methods based on the sway and tilt angle of the tower top, such as Chinese Patent CN111594391A published on August 28, 2020, which discloses an online monitoring method for the tilt angle of a wind turbine tower. This method installs tilt angle sensors and displacement sensors on the top of the tower, and achieves tower verticality analysis and assessment of uneven settlement of the tower foundation by measuring the sway displacement and tilt angle distribution of the tower. In addition, the wind turbine tower condition monitoring systems already equipped on the market also mainly adopt this technical approach.

[0005] While these methods can reflect the tower foundation condition to some extent, they are a lagging monitoring approach. The system only triggers an alarm when significant uneven settlement has occurred in the tower foundation, leading to a measurable tilt angle in the tower. This method cannot directly detect the root causes of settlement or tilting, namely the dynamic overturning moment and eccentric load acting on the tower foundation. Furthermore, the tilt sensor at the tower top is highly susceptible to interference from the tower's own elastic bending deformation and nacelle vibration, resulting in limited measurement accuracy.

[0006] (2) A local monitoring method based on anchor cable (anchor bolt) tension: by installing a cable force sensor on the anchor cable, the tension data of the anchor cable is collected in real time to identify abnormal tension fluctuations and situations exceeding the set threshold.

[0007] These methods can only reflect the local stress state of one or a few anchor cables, and cannot synthesize and calculate the magnitude and direction of the overturning moment on the entire tower foundation. When the tension of anchor cables in multiple directions changes simultaneously, it is impossible to determine whether this is caused by an overturning moment in a single direction or by the superposition of loads in multiple directions, nor can it give the precise direction of the load.

[0008] (3) Displacement monitoring method based on tower flange gap: Some existing technical solutions install displacement sensors at the tower flange connection and determine the tower connection status by monitoring the gap change between adjacent flanges. When the flange gap exceeds a preset threshold, an early warning is issued.

[0009] This type of method also falls under the category of consequence monitoring. Changes in flange clearance are usually caused by loose bolt preload or structural damage, at which point the problem has already occurred. This method cannot provide preventative warnings before problems occur, nor can it provide real-time information on the external loads on the tower base.

[0010] (4) Direct strain / stress monitoring method for foundations: The working condition of the foundation is assessed by measuring the stress and strain inside the foundation by embedding strain gauges or stress gauges in the foundation concrete.

[0011] These methods involve direct monitoring and can theoretically detect load changes. However, because concrete is a nonlinear material, its stress-strain relationship is significantly affected by factors such as temperature, humidity, and creep. Furthermore, point sensors can only acquire localized stress at the installation location, failing to comprehensively reflect the load distribution of the tower foundation in a 360° direction, and easily missing ultimate loads in specific directions. Additionally, large-scale post-construction drilling for installation on existing foundations is extremely difficult and may damage the foundation structure itself.

[0012] In summary, existing technologies lack a system and method capable of directly and online real-time monitoring of the loads on wind turbine tower foundations, particularly the magnitude and direction of the combined overturning moment. This results in problems such as monitoring lag, incomplete information, and susceptibility to interference in current tower foundation safety status assessments. Summary of the Invention

[0013] The purpose of this invention is to provide an online monitoring system and method for wind turbine tower foundation load, which can solve the problem in the prior art that it is impossible to directly and online monitor the overturning moment and its direction of action on the tower foundation; This invention provides an online monitoring system for wind turbine tower foundation loads, comprising: The tower foundation ring strain sensing array includes distributed fiber optic strain sensors arranged in a ring on the outer wall of the tower foundation ring, near the interface between the foundation ring and the concrete foundation platform, for continuously sensing the axial strain at each point within the foundation ring range and outputting a one-dimensional strain sequence along the fiber length direction. The tower foundation anchor bolt strain sensing array includes multiple fiber optic strain sensors, which are respectively installed on multiple anchor bolts distributed along the circumference of the tower foundation, for measuring the axial strain of the anchor bolts; A distributed fiber optic strain demodulator, connected to the distributed fiber optic strain sensor, is used to synchronously demodulate the axial strain and temperature values ​​at various points along the fiber. A fiber optic grating demodulator is connected to each of the fiber optic grating strain sensors and is used to demodulate the strain values ​​of each strain sensor. The computing acquisition unit is communicatively connected to the distributed fiber strain demodulator and the fiber grating demodulator, respectively, and is used for synchronous data acquisition, packaging and uploading. The monitoring server is configured to receive the one-dimensional strain sequence and synchronized distributed temperature data, perform temperature compensation, and convert it into an axial strain function in the angular domain using physical markers on the optical fiber. Solve for the uniform axial strain components caused by the vertical load at the current moment. Amplitude of axial strain in bending caused by overturning moment and the angle of the direction of the overturning moment ; Receive the axial strain data of the anchor bolts, and combine it with and The final overturning moment amplitude and direction parameters are obtained by performing calculations. Determine the reference strain for vertical load , and in conjunction with the above Calculate the resultant force of the real-time vertical load.

[0014] Furthermore: Theoretical axial strain of the foundation ring at angle θ for: .

[0015] Furthermore, the distributed optical fiber strain sensor is arranged in a ring around the outer wall of the base ring for a full circumference, and is provided with physical markers in corresponding directions.

[0016] Furthermore, the fiber optic strain sensors are arranged in groups on multiple anchor bolts evenly distributed along the circumference, with each group containing at least two sensors installed at different heights on the same anchor bolt.

[0017] Furthermore, solve for the current moment. , and Specifically, the process involves: discretizing the annular region into N equal-angle sectors, and calculating the average measured axial strain within each sector i. ; Construct the objective function:

[0018] An iterative optimization algorithm is used to find the parameter combination that minimizes the objective function. , , ).

[0019] Furthermore, the monitoring server specifically performs the following steps when calculating the final overturning moment amplitude and direction parameters: For the k-th anchor bolt, its theoretical axial strain Calculate using the following formula:

[0020] in Let be the azimuth angle of the bolt. , The load transfer factor is determined through calibration; Measure the strain of the anchor bolts The difference between the theoretical axial strain and the strain is used as a constraint term to construct a fusion objective function for solving, and the final overturning moment is output:

[0021] in These are calibration coefficients related to the bending stiffness of the foundation ring section.

[0022] Furthermore, determine the reference strain for the vertical load. Specific execution details: Continuously receive wind speed and operating status data from the wind turbine system; When the conditions are met simultaneously—wind speed continuously lower than the cut-in wind speed, wind turbine shutdown, and duration exceeding a preset threshold—the value within the current time window is taken. The average value was calculated and corrected to a standard temperature using the distributed temperature data, serving as the new reference strain for vertical load. ; Real-time vertical load resultant force:

[0023] in Let A be the load calculation coefficient, A be the cross-sectional area of ​​the base ring, and E be the elastic modulus of the steel.

[0024] Furthermore, it also includes a display terminal for visually displaying the real-time overturning moment amplitude, direction, and resultant vertical load, and for issuing an alarm when the overturning moment amplitude exceeds a preset safety threshold.

[0025] This invention provides a method for online monitoring of wind turbine tower foundation load, applied to the aforementioned online monitoring system, characterized by comprising: S1: Obtain the axial strain sequence and temperature sequence within the base ring range by using distributed fiber optic strain sensors arranged in a ring on the outer wall of the base ring. S2: The axial strain of the anchor bolt is measured using a fiber optic strain sensor on the anchor bolt. S3: Solve for the uniform strain component of the vertical load, the amplitude and direction of the bending strain by fitting the axial strain distribution, and calculate the overturning moment by integrating the bolt strain data, and then calculate the resultant force of the vertical load.

[0026] Furthermore, it also includes S4: real-time display and over-limit warning.

[0027] The beneficial effects of this invention are as follows: (1) By deploying distributed fiber optic strain sensors on the outer wall of the foundation ring, the axial strain of the core force transmission component can be directly measured. The tension and compression areas can be linearly and completely sensed, which solves the problem of signal saturation and failure caused by interface separation when measuring pressure at the contact surface in the prior art. This ensures that the system can still work normally under the overturning moment condition and realizes direct and proactive monitoring.

[0028] (2) The direction and magnitude of the overturning moment are solved by fitting the strain distribution of the entire circumference, and the strain data of the anchor bolts are introduced for redundancy verification, which overcomes the limitations of the single sensing system and ensures measurement accuracy and long-term reliability. At the same time, the resultant force of the vertical load is directly calculated from the uniform strain components, which solves the problem that the vertical force and bending moment cannot be decoupled in the traditional method.

[0029] (3) The distributed optical fiber in the ring layout realizes continuous sensing without blind spots in 360°. Load changes in different directions can be effectively captured, which makes up for the defect of point sensors that may miss the ultimate load in a specific direction.

[0030] (4) The vertical load reference is automatically updated by utilizing the low wind speed shutdown window, and the temperature measurement capability of the distributed optical fiber is introduced for real-time temperature compensation, which effectively eliminates the impact of temperature changes and slow foundation settlement on long-term monitoring accuracy and ensures the measurement stability of the system during its life cycle. Attached Figure Description

[0031] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0032] Figure 1 This is a schematic diagram of the overall system composition of the present invention; Figure 2 A schematic diagram showing the locations of the distributed fiber optic strain sensor and the fiber optic grating strain sensor; Figure 3 This refers to the ring-shaped arrangement of distributed fiber optic strain sensors on the outer wall of the base ring. Figure 4 This is a schematic diagram showing the installation of a fiber optic strain sensor on an anchor bolt. Figure 5 The cosine distribution law of the axial strain of the foundation ring under the action of overturning moment; Figure 6 Here is a flowchart of the load inversion procedure; Figure 7 A flowchart of the adaptive window self-calibration method; Explanation of reference numerals in the attached figures: 1-Tower; 2-Foundation ring; 3-Concrete foundation platform; 4-Distributed fiber optic strain sensor; 5-Anchor bolt; 6-Fiber grating strain sensor; 7-Physical marker point; 8-Distributed fiber optic strain demodulator; 9-Fiber grating demodulator; 10-Computational data acquisition unit; 11-Monitoring server; 12-Display terminal. Detailed Implementation

[0033] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0035] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified. Furthermore, the terms "installed," "connected," and "linked" should be interpreted broadly; for example, they may refer to a fixed connection, a detachable connection, or an integral connection; they may refer to a mechanical connection or an electrical connection; they may refer to a direct connection or an indirect connection through an intermediate medium; and they may refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0036] Example 1 This embodiment provides an online monitoring system for the load on the foundation of a wind turbine tower.

[0037] like Figures 1-7As shown in the figure, on the outer side wall of the foundation ring 2 of the tower barrel 1, adjacent to the junction between the foundation ring 2 and the concrete foundation cap 3, a distributed optical fiber strain sensor 4 is arranged annularly along the circumference. The foundation ring 2 is a steel cylinder of the tower barrel 1 inserted into the concrete foundation cap 3, configured to transmit loads. At this selected position, under the action of overturning moment and vertical force, the axial strain of the foundation ring 2 follows the plane section assumption, and can sense both tensile and compressive strains without measurement blind zones. The distributed optical fiber strain sensor 4 adopts a sensing optical fiber based on Optical Frequency Domain Reflectometry (OFDR) technology, such as the sensing optical fiber matched with the LUNA ODiSI series. A metal ring physical marking point 7 is provided on the optical fiber at the position corresponding to the true north direction for spatial positioning. The marking point can be a metal ring fixed on the optical fiber sheath or an identifiable feature formed by the bending radius of the optical fiber, which corresponds to a clear spatial position reference in the demodulated signal, and is used to convert the one-dimensional optical fiber length coordinate into an angular coordinate. One FBG strain sensor is respectively installed on each of the two upper and lower sections of each anchor bolt 5 at the four orientations of 0°, 90°, 180°, and 270°, with a total of 8 sensors. By installing at least two sensors at different heights of the same bolt, the interference of possible bending effect of the bolt on axial strain measurement can be eliminated, so as to accurately obtain the strain purely generated by the axial force. The sensors are fixed on the polished and derusted bolt surface through epoxy resin adhesive.

[0038] The distributed optical fiber strain demodulator 8 and the fiber Bragg grating demodulator 9 are installed in the tower bottom control cabinet. The demodulator synchronously acquires the strain and temperature values of each point, and the demodulator acquires the FBG wavelength drift and converts it into strain. Both of them send the data to the computing collector 10. After the computing collector 10 completes time synchronization and packaging, the data is uploaded to the monitoring server 11 through the wind farm ring network.

[0039] The monitoring server 11 runs a load inversion program, and the specific steps are as follows: Step 1: Correct the strain of each point to the standard temperature by using the distributed temperature data. Convert the one-dimensional strain sequence into an angular domain function through the physical marking point 7 . The theoretical strain model on which the present invention is based is , which is established based on the plane section assumption of mechanics of materials and Hooke's law. Under the combined action of vertical load and overturning moment, the axial strain of the foundation ring 2 presents a cosine curve with DC bias in the circumferential direction. Wherein, the uniform component directly reflects the vertical load, the amplitude of the cosine component is proportional to the magnitude of the overturning moment, and the phase angle accurately indicates the acting direction of the overturning moment.

[0040] Step 2: Fitting and solving of the strain distribution. The circumference is discretized into 72 sectors, and the average strain of each sector is calculated . Construct the objective function Iterative optimization algorithms, such as the Levenberg-Marquardt algorithm, are used to solve for the optimal parameter combination to obtain the uniform axial strain components induced by the vertical load. The amplitude of axial strain caused by overturning moment and the angle of the direction of the overturning moment By utilizing strain information across the entire circumference, it exhibits resistance to localized noise interference.

[0041] Step 3: When monitoring server 11 calculates the final overturning moment amplitude and direction parameters, it introduces four sets of strain data from anchor bolts 5 for redundant calculation and cross-validation. For the k-th anchor bolt 5, its theoretical axial strain is calculated according to the theoretical strain formula. ,in Let be the azimuth angle of the bolt. , The load transfer factor is determined through finite element analysis or field calibration; the measured strain of anchor bolt 5 is used. The difference between the theoretical strain and the actual strain is used as a constraint term to construct a fusion objective function for solving, and the final overturning moment is output. and direction ,in This is a calibration factor related to the bending stiffness of section 2 of the foundation ring. Redundancy design ensures that reliable monitoring results can still be provided even if the performance of a single sensor system degrades.

[0042] Step 4: Determine the reference strain for vertical load To address the long-term drift issues caused by slow foundation settlement, material creep, and temperature changes, this invention employs an adaptive window self-calibration method. The program continuously receives wind speed data from the wind turbine data acquisition and monitoring control system. When the wind speed is <3m / s and the turbine has been shut down for more than 30 minutes, the data within the current time window is used. The average value was calculated and corrected to a standard temperature (e.g., 20°C) using temperature data synchronously measured via distributed optical fibers, and used as the new reference strain for vertical load. The real-time vertical resultant force is generated by... The calculation shows that, among which For load calculation, A is the cross-sectional area of ​​the base ring 2, and E is the elastic modulus of the steel of the base ring 2, which is usually taken as 206 GPa.

[0043] Step 5: The display terminal 12 refreshes in real time, and an audible and visual alarm is triggered when the overturning moment exceeds the design limit by 80%.

[0044] Example 2 This embodiment provides a monitoring method, the specific steps of which are as follows: S1: The axial strain sequence and temperature sequence within the range of the base ring 2 are obtained by using distributed optical fiber strain sensors 4 arranged in a ring on the outer wall of the base ring 2. S2: Measure the axial strain of the bolt 5 using the fiber optic strain sensor 6 on the anchor bolt 5; S3: Solve for the uniform strain component of the vertical load, the amplitude and direction of the bending strain by fitting the axial strain distribution, and calculate the overturning moment by integrating the bolt strain data, and then calculate the resultant force of the vertical load; S4: Display load parameters in real time on display terminal 12 and issue a warning when the limit is exceeded.

[0045] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An online monitoring system for wind turbine tower foundation load, characterized in that, include; The tower foundation ring strain sensing array includes distributed fiber optic strain sensors arranged in a ring on the outer wall of the tower foundation ring, near the interface between the foundation ring and the concrete foundation platform, for continuously sensing the axial strain at each point within the foundation ring range and outputting a one-dimensional strain sequence along the fiber length direction. The tower foundation anchor bolt strain sensing array includes multiple fiber optic strain sensors, which are respectively installed on multiple anchor bolts distributed along the circumference of the tower foundation, for measuring the axial strain of the anchor bolts; A distributed fiber optic strain demodulator, connected to the distributed fiber optic strain sensor, is used to synchronously demodulate the axial strain and temperature values ​​at various points along the fiber. A fiber optic grating demodulator is connected to each of the fiber optic grating strain sensors and is used to demodulate the strain values ​​of each strain sensor. The computing acquisition unit is communicatively connected to the distributed fiber strain demodulator and the fiber grating demodulator, respectively, and is used for synchronous data acquisition, packaging and uploading. The monitoring server is configured to receive the one-dimensional strain sequence and synchronized distributed temperature data, perform temperature compensation, and convert it into an axial strain function in the angular domain using physical markers on the optical fiber. Solve for the uniform axial strain components caused by the vertical load at the current moment. Amplitude of axial strain in bending caused by overturning moment and the angle of the overturning moment ; Receive the axial strain data of the anchor bolts, and combine it with and The final overturning moment amplitude and direction parameters are obtained by performing calculations. Determine the reference strain for vertical load , and in conjunction with the above Calculate the resultant force of the real-time vertical load.

2. The online monitoring system for wind turbine tower foundation load according to claim 1, characterized in that, Theoretical axial strain of the foundation ring at angle θ for: 。 3. The online monitoring system for wind turbine tower foundation load according to claim 1, characterized in that, The distributed fiber optic strain sensors are arranged in a ring around the outer wall of the base ring, and are equipped with physical markers in corresponding directions.

4. The online monitoring system for wind turbine tower foundation load according to claim 1, characterized in that, The fiber optic strain sensors are arranged in groups on multiple anchor bolts that are evenly distributed along the circumference, with each group containing at least two sensors installed at different heights on the same anchor bolt.

5. The online monitoring system for wind turbine tower foundation load according to claim 4, characterized in that, Solve for the current time. , and At that time, the specific execution is as follows: The annular region is discretized into N equal-angle sectors, and the average measured axial strain in each sector i is calculated. ; Construct the objective function: An iterative optimization algorithm is used to find the parameter combination that minimizes the objective function. , , ).

6. The online monitoring system for wind turbine tower foundation load according to claim 1, characterized in that, The monitoring server specifically executes the following when calculating the final overturning moment amplitude and direction parameters: For the k-th anchor bolt, its theoretical axial strain Calculate using the following formula: in Let be the azimuth angle of the bolt. , The load transfer factor is determined through calibration; Measure the strain of the anchor bolts The difference between the theoretical axial strain and the strain is used as a constraint term to construct a fusion objective function for solving, and the final overturning moment is output: in These are calibration coefficients related to the bending stiffness of the foundation ring section.

7. The online monitoring system for wind turbine tower foundation load according to claim 1, characterized in that, Determine the reference strain for vertical load Specific execution details: Continuously receive wind speed and operating status data from the wind turbine system; When the conditions are met simultaneously—wind speed continuously lower than the cut-in wind speed, wind turbine shutdown, and duration exceeding a preset threshold—the value within the current time window is taken. The average value was calculated and corrected to a standard temperature using the distributed temperature data, serving as the new reference strain for vertical load. ; Real-time vertical load resultant force: in Let A be the load calculation coefficient, A be the cross-sectional area of ​​the base ring, and E be the elastic modulus of the steel.

8. The online monitoring system for wind turbine tower foundation load according to any one of claims 1-7, characterized in that, It also includes a display terminal for visually displaying the real-time overturning moment amplitude, direction, and resultant vertical load, and for issuing an alarm when the overturning moment amplitude exceeds a preset safety threshold.

9. A method for online monitoring of wind turbine tower foundation load, applied to the online monitoring system described in any one of claims 1 to 8, characterized in that, include: S1: Obtain the axial strain sequence and temperature sequence within the base ring range by using distributed fiber optic strain sensors arranged in a ring on the outer wall of the base ring. S2: The axial strain of the anchor bolt is measured using a fiber optic strain sensor on the anchor bolt. S3: Solve for the uniform strain component of the vertical load, the amplitude and direction of the bending strain by fitting the axial strain distribution, and calculate the overturning moment by integrating the bolt strain data, and then calculate the resultant force of the vertical load.

10. The online monitoring method according to claim 9, characterized in that, It also includes S4: real-time display and over-limit warning.

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