Aircraft direct current arc fault detection method, system, medium and equipment

Abstract

An aircraft DC arc fault detection method, system, medium and device, in the method, current data of a time window of a loop is measured, an average value of current in the time window is calculated, a peak-to-peak value and a spectral area value are calculated after the current data passes through a high-pass filter, and the peak-to-peak value is a difference value between a maximum value and a minimum value of current in the time window; judging whether the circuit is disconnected or not by using the effective value, judging the change trend of the current of the loop, and providing a basis for subsequent threshold selection; calculating the ratio of the peak-to-peak value and the spectral area to the historical value, respectively presetting the threshold values of different peak-to-peak value and spectral area ratios according to the fault characteristics of different types of arcs, comparing the ratios with the threshold values, and adding one to a corresponding marker when a certain ratio reaches the threshold value; and selecting a corresponding fault judgment condition to judge whether an arc fault occurs or not according to the state of each current marker in combination with the change trend of the current average value.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft DC arc faults, and in particular to an aircraft DC arc fault detection method, system, medium and equipment. Background Art

[0002] With the development of more-electric aircraft and all-electric aircraft, aircraft power distribution systems have become more complex, and the probability of line failures will also increase. Aviation cables mostly operate in a vibrating environment. Due to the frequent takeoffs and landings of aircraft, cables are usually located in locations with large changes in temperature and humidity. These factors will cause loose wiring and insulation damage, which will cause arc faults. The arc will generate high temperatures, which can easily ignite other onboard equipment on the aircraft, causing fires and posing huge safety hazards to the aircraft and the personnel on board. When an arc fault occurs in the DC electrical system of an aircraft, it is difficult for the existing solid-state power controller (SSPC) to achieve reliable online detection of the arc. The high temperature generated by the long-term arc fault will further cause electrical fires, seriously affecting the safety of onboard equipment and personnel. Since the current value of the series arc is less than the normal current, the traditional overcurrent protection device cannot effectively detect the fault, and a fault arc detection device needs to be added. Therefore, the research on the detection technology of series fault arcs in aviation systems is of great significance.

[0003] The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Summary of the invention

[0004] The present invention provides an aircraft DC arc fault detection method, system, medium and equipment. By monitoring the current signal of the system loop, calculating the peak-to-peak value and the spectrum area of ​​the current signal, and comparing the calculated characteristic value ratio with a threshold value by means of a sliding time window, the aircraft DC arc fault can be accurately and reliably detected, which solves the problem that the existing aircraft arc fault detection method is difficult to quickly and accurately realize fault detection. The proposed method can adapt to different fault types such as series, parallel and vibration arc.

[0005] A method for detecting a DC arc fault in an aircraft includes:

[0006] Measuring current data of a time window of a circuit simulating a DC arc fault of an aircraft and calculating the average value of the current in the time window, and calculating the peak-to-peak value and spectrum area value of the current data after passing through a high-pass filter, wherein the peak-to-peak value is the difference between the maximum value and the minimum value of the current in a time window;

[0007] The current average value is used to determine whether the circuit is open. The threshold interval is selected according to the change of the average value. When the average value increases, the threshold used to determine the parallel fault is selected for fault judgment. If the average value decreases, the threshold used to determine the series fault is selected for fault judgment.

[0008] Calculate the ratio of peak-to-peak value and spectrum area to their historical values;

[0009] According to the fault characteristics of different types of arcs and preset thresholds of different peak-to-peak value and spectrum area ratios, the ratio is compared with the threshold, and when the ratio reaches the threshold, the corresponding flag value is increased by one;

[0010] According to the current status of each indicator and the changing trend of the current average value, the corresponding fault judgment condition is selected to determine whether an arc fault occurs.

[0011] In the aircraft DC arc fault detection method, the time window is 10ms.

[0012] In the aircraft DC arc fault detection method, the current data is passed through a high-pass filter with a cut-off frequency of 100 Hz to calculate the peak-to-peak value and the spectrum area value.

[0013] In the aircraft DC arc fault detection method, calculating the ratio of the peak-to-peak value and the spectrum area to their historical values ​​includes comparing the peak-to-peak value and the spectrum area of ​​the latest time window obtained over time with the historical average value of the peak-to-peak value and the spectrum area of ​​5 consecutive time windows before 0.5 seconds.

[0014] In the aircraft DC arc fault detection method, different types of arcs include series arcs, parallel arcs and vibration arcs.

[0015] In the aircraft DC arc fault detection method, the calculation formula of the spectrum area value is as follows:

[0016] ,

[0017] ,

[0018] Where I(F) is the spectrum obtained after fast Fourier transform of each time window, n and m are the data point numbers corresponding to the start frequency and end frequency of the horizontal axis of the spectrum area to be calculated; f0 is the frequency resolution of the spectrum after fast Fourier transform of the current, f s is the sampling rate, N is the number of sampling points, and the frequency resolution reflects the energy of a certain frequency band of the current.

[0019] In the aircraft DC arc fault detection method, when the arc fault does not occur, the ratio of the peak-to-peak value to its historical value is close to 1 and the ratio of the spectrum area value to its historical value is close to 1.

[0020] An aircraft DC arc fault detection system comprises:

[0021] circuit, which is used to simulate aircraft DC arc faults;

[0022] A measuring unit, which is used to connect the loop and measure the current data of a time window of the loop and calculate the average value of the current in the time window, and calculate the peak-to-peak value and spectrum area value of the current data after passing through a high-pass filter, and the peak-to-peak value is the difference between the maximum value and the minimum value of the current in a time window;

[0023] A judgment unit, which is used to use the effective value to judge whether the circuit is open and to judge the change trend of the current in the loop, so as to provide a basis for the subsequent threshold selection;

[0024] A calculation unit is used to calculate the ratio of the peak-to-peak value and the spectrum area to their historical values, and compare the ratio with the threshold according to the fault characteristics of different types of arcs and different preset thresholds of the peak-to-peak value and the spectrum area ratio. When a certain ratio reaches the threshold, the corresponding mark value is increased by one; according to the current status of each mark value and the changing trend of the current average value, the corresponding fault judgment condition is selected to determine whether an arc fault occurs.

[0025] A computer storage medium includes computer instructions, which, when executed on a computer, cause the computer to execute the method described above.

[0026] An electronic device, comprising:

[0027] A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein:

[0028] When the processor executes the program, the method described is implemented.

[0029] Compared with the prior art, the present invention has the following advantages: the present invention proposes peak-to-peak value and spectrum area as key indicators for realizing arc fault detection; the characteristic value is compared with the historical value in a sliding time window manner to realize the normalization of the characteristic value, and fault detection is realized by threshold comparison; the fault characteristics of three different arc fault types, namely series, parallel and vibration arc, are considered, and an actual load type circuit on board is built, which can better simulate the special environment of arc fault on board, lay the foundation for the proposal of the detection method and has high detection accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] By reading the detailed description of the preferred specific embodiments below, various other advantages and benefits of the present invention will become clear to those of ordinary skill in the art. The drawings in the specification are only for the purpose of illustrating the preferred embodiments and are not considered to be limitations of the present invention. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative work. Moreover, the same reference numerals are used to represent the same components throughout the drawings.

[0031] In the attached picture:

[0032] Figure 1 It is a flow chart of a method for detecting DC arc faults in aircraft;

[0033] Figures 2(a) to 2(c) are schematic diagrams of arc fault generating devices, wherein Figure 2(a) is a series arc generating device, Figure 2(b) is a parallel arc generating device, and Figure 2(c) is a vibration arc generating device;

[0034] Figure 3 It is a schematic diagram of a capacitive load circuit;

[0035] Figure 4 (a) and Figure 4 (b) are schematic diagrams of the current time domain waveform and spectrum waveform before and after the arc occurs. Figure 4 (a) is a 28V, 30A resistive load, and Figure 4 (b) is a 28V, 20A resistive load;

[0036] Figures 5(a) to 5(d) are comparison diagrams of the spectrum area ratios before and after the fault and load shedding. Figure 5(a) shows a 28V series arc and a vibration arc, Figure 5(b) shows a 28V parallel arc, Figure 5(c) shows a 270V series arc and a vibration arc, and Figure 5(d) shows a 270V series arc and a vibration arc.

[0037] The present invention is further explained below in conjunction with the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0038] The specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the specific embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0039] It should be noted that certain words are used in the specification and claims to refer to specific components. Those skilled in the art should understand that technicians may use different nouns to refer to the same component. This specification and claims do not use the difference in nouns as a way to distinguish components, but use the difference in the functions of the components as the criterion for distinction. As mentioned throughout the specification and claims, "including" or "comprising" is an open term, so it should be interpreted as "including but not limited to". The subsequent description of the specification is a preferred embodiment of the present invention, but the description is based on the general principles of the specification and is not intended to limit the scope of the present invention. The scope of protection of the present invention shall be determined by the attached claims.

[0040] To facilitate understanding of the embodiments of the present invention, further explanation will be given below by taking specific embodiments as examples in conjunction with the accompanying drawings, and each of the accompanying drawings does not constitute a limitation on the embodiments of the present invention.

[0041] like Figure 1 As shown in FIG5( d ), the aircraft DC arc fault detection method includes the following steps:

[0042] The current data of a time window of the loop is measured and the average current value in the time window is calculated. The peak-to-peak value and the spectrum area value are calculated after the current data passes through a high-pass filter. The peak-to-peak value is the difference between the maximum and minimum current values ​​in a time window. The loop includes a power supply, a solid-state power controller SSPC for aircraft, and an experimental load built according to the actual load type of the aircraft, which includes resistive, capacitive and inductive loads, and an arc generating device. The solid-state power controller SSPC, series arc and vibration arc generating device are connected in series in the loop, and the parallel arc generating device is connected in parallel with part of the load (different types of arc generating devices are used in experiments with different arc types).

[0043] The current average value is used to determine whether the circuit is open. The threshold range is selected according to the change of the average value. When the average value increases, the threshold used to determine parallel faults is selected for fault judgment. If the average value decreases, the threshold used to determine series faults is selected for fault judgment. Furthermore, if the average value is less than 0.3A, it is considered to be open. When the average value increases, the algorithm will select the threshold used to determine parallel faults for fault judgment. If the average value decreases, the threshold used to determine series faults is selected for fault judgment.

[0044] Calculate the ratio of peak-to-peak value and spectrum area to their historical values;

[0045] According to the fault characteristics of different types of arcs, different peak-to-peak value and spectrum area ratio thresholds are preset respectively, and the ratio is compared with the threshold. When a certain ratio reaches the threshold, the corresponding flag value is increased by one;

[0046] According to the current status of each flag, combined with the trend of the current average value, the corresponding fault judgment condition is selected to determine whether an arc fault occurs. Flag1s and flag2s will increase according to whether p2p and freqi exceed the threshold set for series arc judgment. When the two series arc judgment flags flag1s and flag2s exceed the fault judgment thresholds sf1 and sf2 and the current decreases according to the average value, it is considered that a series arc fault has occurred. The judgment process of parallel arc and vibration arc is the same as that of series arc, except that the relevant judgment thresholds are different.

[0047] Figure 1 The middle right half indicates that the arc fault is judged according to the changing trend of the current and whether the peak-to-peak value and the spectrum area exceed the threshold. S1, S2 and S3 are the peak-to-peak value and the spectrum area thresholds of the series arc fault, V1 and V2 are the peak-to-peak value and the spectrum area thresholds of the parallel arc fault, V1 and V2 are the peak-to-peak value and the spectrum area thresholds of the vibration arc fault. When the ratio of the peak-to-peak value P2P and the spectrum area Freqi reaches the threshold judgment standard, the corresponding fault judgment flags Flag1s, Flag2s, Flag1p, Flag2p and Flagv are respectively operated accordingly, and the series and parallel arc faults are judged in combination with the series and parallel flags of the circuit current decrease and increase. When the corresponding fault judgment flags reach the threshold intervals of SF1, SF2, PF1, PF2 and VF respectively, it is considered that an arc fault has occurred.

[0048] In a preferred implementation of the aircraft DC arc fault detection method, the time window is 10 ms.

[0049] In a preferred implementation of the aircraft DC arc fault detection method, the current data is passed through a high-pass filter with a cut-off frequency of 100 Hz and then the peak-to-peak value and the spectrum area value are calculated.

[0050] In a preferred implementation of the aircraft DC arc fault detection method, calculating the ratio of the peak-to-peak value and the spectrum area to their historical values ​​includes comparing the peak-to-peak value and the spectrum area of ​​the latest time window obtained over time with the historical average value of the peak-to-peak value and the spectrum area of ​​5 consecutive time windows before 0.5 seconds.

[0051] In a preferred implementation of the aircraft DC arc fault detection method, the different types of arcs include series arcs, parallel arcs and vibration arcs.

[0052] In a preferred implementation of the aircraft DC arc fault detection method, the calculation formula of the spectrum area value is as follows:

[0053] ,

[0054] ,

[0055] Where I(F) is the spectrum obtained after fast Fourier transform of each time window, n and m are the data point numbers corresponding to the start frequency and end frequency of the horizontal axis of the spectrum area to be calculated; f0 is the frequency resolution of the spectrum after fast Fourier transform of the current, f s is the sampling rate, N is the number of sampling points, and the frequency resolution reflects the energy of a certain frequency band of the current.

[0056] In a preferred implementation of the aircraft DC arc fault detection method, when the arc fault does not occur, the ratio of the peak-to-peak value to its historical value is close to 1 and the ratio of the spectrum area value to its historical value is close to 1.

[0057] An aircraft DC arc fault detection system comprises:

[0058] circuit, which simulates an aircraft DC arc fault;

[0059] A measuring unit connected to the loop and measuring the current data of a time window of the loop and calculating the average value of the current in the time window, wherein the peak-to-peak value and the spectrum area value are calculated after the current data passes through a high-pass filter, and the peak-to-peak value is the difference between the maximum value and the minimum value of the current in a time window;

[0060] The judgment unit uses the effective value to judge whether the circuit is open and the change trend of the current in the loop to provide a basis for the subsequent threshold selection;

[0061] A calculation unit calculates the ratio of the peak-to-peak value and the spectrum area to their historical values, presets different thresholds for the peak-to-peak value and the spectrum area ratio according to the fault characteristics of different types of arcs, compares the ratio with the threshold, and when a certain ratio reaches the threshold, increases the corresponding mark value by one; according to the current status of each mark value and the changing trend of the current average value, selects the corresponding fault judgment condition to determine whether an arc fault occurs.

[0062] A computer storage medium includes computer instructions, which, when executed on a computer, cause the computer to execute the method described above.

[0063] An electronic device, comprising:

[0064] A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein:

[0065] When the processor executes the program, the method described is implemented.

[0066] In one embodiment, the method includes,

[0067] 1. Measure the current data of a time window of the loop. The time window size is selected as 10ms, and the average current value in the time window is calculated. In order to eliminate the influence of the DC component on the characteristic value, the current data is passed through a high-pass filter with a cutoff frequency of 100Hz, and the peak-to-peak value and spectrum area value are calculated;

[0068] 2. Use the effective value to determine whether the circuit is open and the changing trend of the loop current to provide a basis for subsequent threshold selection;

[0069] 3. Calculate the ratio of the peak-to-peak value and the spectrum area to the historical value by comparing the characteristic value of the latest time window obtained over time with the historical average of the characteristic values ​​of the five consecutive time windows before 0.5 seconds;

[0070] 4. According to the fault characteristics of different types of arcs, different peak-to-peak value and spectrum area ratio thresholds are preset respectively, and the obtained ratio data is compared with the threshold. When a certain ratio reaches the threshold setting requirement, the corresponding flag value is increased by one;

[0071] 5. According to the current status of each mark quantity and the changing trend of the current average value, the corresponding fault judgment condition is selected to determine whether an arc fault occurs. The fault judgment condition sets different threshold intervals according to the characteristics of the three different types of arcs: series, parallel and vibration.

[0072] In one embodiment, as shown in FIG. 2 (a) to FIG. 2 (c), a series, parallel and vibration arc generating device is built, and a specific arc fault is generated by the arc generating device to obtain arc fault data. For example, in the series arc generating device, the device is composed of two electrodes, a stepper motor, a controller, an epoxy resin column and a guide rail. The electrode diameter is 5 mm, and the moving distance and speed are set to 0.2 mm (0.2 mm / s) and 1 mm (2 mm / s) respectively according to the voltage of 28 V or 270 V. When the two electrodes are separated, if the current on the electrode is greater than the arc starting current, an arc will be generated. The differential voltage probe model is Tektronix P5200A (measurement range 0-1300 V, bandwidth 100 MHz), and the current probe model is Chauvin Arnoux E3N (measurement range 0-100 A, bandwidth DC-100 kHz). The oscilloscope model is Rohde-Schwarz RTO1024 (maximum bandwidth 2GHz, maximum sampling rate 10GSa / s), and the sampling frequency is set to 625kHz. To simulate the aircraft electrical system, the DC power supply output voltage is set to 28V and 270V respectively. The solid-state power controller (SSPC) and the arc generator are connected in series in the circuit. According to the aircraft load conditions, the load type is set to pure resistance load and capacitive load. The filter and 270V / 28V DC / DC module are added according to the 28V capacitive load. Each set of experiments is repeated at least 5 times.

[0073] According to the actual voltage level, current range and load type of the onboard DC system, the experimental conditions shown in Tables 1 and 2 were set to test the detection method.

[0074] Table 1 28V voltage level experiment settings

[0075]

[0076] Table 2 270V voltage level experiment settings

[0077]

[0078] The capacitive load is a simulation circuit built according to the actual working load characteristics of the aircraft. The inductive load uses the motor actually used in the aircraft. The capacitive load circuit diagram is as follows: Figure 3 As shown, the current can be adjusted by replacing resistor R2. Figure 3 It represents capacitive load. C1, C2, C3, C4, C5 and the part composed of resistors, diodes and C6 all play the role of maintaining the load supply voltage for a short time when the power is switched on the aircraft. U1 is a DC filter that can suppress noise on the DC power line. R2 is the load resistor.

[0079] The peak-to-peak value and spectrum area are selected as the criterion features. The peak-to-peak value is the difference between the maximum and minimum current values ​​in a time window. The spectrum area is calculated as follows:

[0080] (1)

[0081] (2)

[0082] Where I(F) is the spectrum obtained after fast Fourier transform (FFT) of each time window, n and m are the data point numbers corresponding to the start frequency and end frequency of the horizontal axis of the spectrum area to be calculated; f0 is the frequency resolution of the spectrum after FFT of the current, f s is the adoption rate, N is the number of sampling points, and this characteristic quantity can reflect the energy size of a certain frequency band of the current. The latest peak-to-peak value and spectrum area values ​​obtained can be normalized by comparing them with the historical average values. When the arc fault does not occur, the current is relatively stable, and the ratio of the peak-to-peak value to the spectrum area is close to 1. As shown in Figure 4 (a) and Figure 4 (b), after the arc fault occurs, the current instability increases, and the high-frequency component increases significantly. At this time, the peak-to-peak value and spectrum area ratio will increase significantly. The waveforms in the large figures of Figure 4 (a) and Figure 4 (b) represent the current time domain waveforms of the series arcing experiment. The arc occurs after 0s. The waveform in the blue dotted box is the spectrum diagram before and after the arc fault occurs. The red line represents the fault current spectrum, and the black line represents the normal current spectrum. The acquisition method is to take a time window of the same length before and after the fault for fast Fourier transform (FFT) and plot it on the same coordinate axis.

[0083] As shown in Figure 5 (a) to Figure 5 (d), the scatter plots of the spectrum area ratio under different experimental conditions are shown. According to the statistical results, the reasonable threshold value can provide an effective basis for the judgment of arc fault. Figure 5 (a) to Figure 5 (d) are scatter plots of the spectrum area ratio of arc fault and load shedding experimental fault, and before and after load shedding. The legend in the upper right corner of the figure indicates the working conditions represented by different colors of the scatter plot, the horizontal axis represents the experimental current level, and the vertical axis is the ratio size.

[0084] Under the test conditions shown in Table 1, arc monitoring accuracy rates of 97.08% (233 / 240) and 97.85% (182 / 186) were achieved at 28 V and 270 V voltage levels, respectively, and load shedding false detection rates of 0% (0 / 20) and 0% (0 / 19).

[0085] Although the embodiments of the present invention are described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific embodiments and application fields, and the above specific embodiments are only illustrative and instructive, rather than restrictive. A person of ordinary skill in the art can also make many forms under the guidance of this specification and without departing from the scope of protection of the claims of the present invention, all of which belong to the protection of the present invention.

Claims

1. A method for detecting DC arc faults in aircraft, characterized in that: The steps include: Measuring current data of a time window of a circuit simulating a DC arc fault of an aircraft and calculating the average value of the current in the time window, and calculating the peak-to-peak value and spectrum area value of the current data after passing through a high-pass filter, wherein the peak-to-peak value is the difference between the maximum value and the minimum value of the current in a time window; The current average value is used to determine whether the circuit is open. The threshold interval is selected according to the change of the average value. When the average value increases, the threshold used to determine the parallel fault is selected for fault judgment. If the average value decreases, the threshold used to determine the series fault is selected for fault judgment. Calculate the ratio of peak-to-peak value and spectrum area to their historical values; According to the fault characteristics of different types of arcs and preset thresholds of different peak-to-peak value and spectrum area ratios, the ratio is compared with the threshold, and when the ratio reaches the threshold, the corresponding flag value is increased by one; According to the current status of each indicator and the changing trend of the current average value, the corresponding fault judgment condition is selected to determine whether an arc fault occurs.

2. The aircraft DC arc fault detection method according to claim 1, characterized in that: Preferably, the time window is 10 ms.

3. The aircraft DC arc fault detection method according to claim 1, characterized in that: The current data was passed through a high-pass filter with a cutoff frequency of 100 Hz and then the peak-to-peak value and the spectrum area value were calculated.

4. The aircraft DC arc fault detection method according to claim 1, characterized in that Calculating the ratio of the peak-to-peak value and the spectral area to their historical values ​​includes comparing the peak-to-peak value and the spectral area of ​​the latest time window acquired over time with the historical average values ​​of the peak-to-peak value and the spectral area of ​​5 consecutive time windows before 0.5 s.

5. The aircraft DC arc fault detection method according to claim 1, characterized in that: Different types of arcs include series arcs, parallel arcs, and oscillating arcs.

6. The aircraft DC arc fault detection method according to claim 1, characterized in that: When an arc fault does not occur, the ratio of the peak-to-peak value to its historical value is close to 1 and the ratio of the spectrum area value to its historical value is close to 1.

7. An aircraft DC arc fault detection system, characterized in that: These include, circuit, which is used to simulate aircraft DC arc faults; A measuring unit, which is used to connect the loop and measure the current data of a time window of the loop and calculate the average value of the current in the time window, and calculate the peak-to-peak value and spectrum area value of the current data after passing through a high-pass filter, and the peak-to-peak value is the difference between the maximum value and the minimum value of the current in a time window; A judgment unit, which is used to use the effective value to judge whether the circuit is open and to judge the change trend of the current in the loop, so as to provide a basis for the subsequent threshold selection; A calculation unit is used to calculate the ratio of the peak-to-peak value and the spectrum area to their historical values, and compare the ratio with the threshold value according to the fault characteristics of different types of arcs and the preset threshold values ​​of the peak-to-peak value and the spectrum area ratio. When the ratio reaches the threshold value, the corresponding mark value is increased by one; according to the current status of each mark value and the changing trend of the current average value, the corresponding fault judgment condition is selected to determine whether an arc fault occurs.

8. A computer storage medium, characterized in that The storage medium includes computer instructions, which, when executed on a computer, enable the computer to execute the method according to any one of claims 1 to 6.

9. An electronic device, characterized in that: The electronic device comprises: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method according to any one of claims 1 to 6 is implemented.

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