A method for constructing a vibration test profile of an airborne equipment of an amphibious aircraft

Abstract

This invention provides a method for constructing a vibration test profile for airborne equipment of amphibious aircraft. The method includes: S1. Delineating the flight phases and regions of the amphibious aircraft; S2. Collecting measured vibration data from the aircraft; S3. Analyzing, processing, and summarizing the measured vibration data; and S4. Constructing a reliability vibration test profile based on the measured vibration data. This invention solves the problem that constructing a reliability vibration test profile based on reference stress is not reasonable or effective enough.

Description

Technical Field

[0001] This invention belongs to the field of amphibious aircraft reliability testing technology, specifically relating to a method for constructing vibration test profiles for airborne equipment of amphibious aircraft. Background Technology

[0002] The reliability of aviation products is a key element in ensuring flight safety, operational efficiency, and user confidence. Reliability testing is of great significance in improving product reliability levels. Reliability testing typically includes tests for temperature, humidity, and vibration. Vibration is usually generated by the operation and movement of the product. Excessive vibration levels can affect flight safety, cause malfunctions in aircraft instruments or onboard equipment, reduce overall aircraft reliability, and consequently increase aircraft maintenance costs. The development of a vibration test profile is fundamental to conducting reliability vibration testing, and the rationality of the vibration test profile determines the effectiveness of the reliability test.

[0003] Amphibious aircraft typically use turboprop engines as their power plant. Existing literature indicates that for turboprop aircraft, the vibrations experienced by their avionics are primarily caused by aerodynamic noise and the rotating pressure field generated by the propeller blades. Current reliability vibration tests for aircraft products are mainly conducted according to GIB 899A and GJB 150.16A. According to GJB 899A, measured or estimated stresses should be used preferentially. If such stress data is unavailable, reference stresses provided by relevant standards are used. However, in actual testing, reference stresses are often directly used, which may result in an inadequate and unreasonable reliability vibration test profile. This makes it difficult to accurately simulate the actual vibration environment of the avionics, affecting the reliability of the equipment. Furthermore, GJB 150.16A primarily differentiates between jet aircraft, propeller aircraft, and helicopters based on their power plants, without specifying particular requirements for amphibious aircraft. However, large amphibious aircraft, due to the unique characteristics of their typical mission profiles, differ from those of general propeller aircraft. In addition to broadband and narrowband random vibrations generated by aerodynamic disturbances and engine operation, amphibious aircraft also experience complex water loads during takeoff and landing on water. The huge impact force generated by these loads can cause vibrations in the fuselage of the aircraft. Therefore, the current main reliability vibration test profile construction methods are not very applicable to the vibration test of airborne equipment of amphibious aircraft. Summary of the Invention

[0004] The present invention aims to provide a method for constructing vibration test profiles for amphibious aircraft airborne equipment. This invention solves the problem that constructing reliability vibration test profiles based on reference stress is not sufficiently reasonable and effective.

[0005] Technical solution. A method for constructing vibration test profiles for airborne equipment of amphibious aircraft, comprising: S1. Flight phases and area divisions for amphibious aircraft; S2. Collect measured vibration data of the aircraft; S3. Analysis, processing, and summarization of measured vibration data; S4. Construct a reliability vibration test profile based on measured vibration data.

[0006] In the aforementioned method for constructing vibration test profiles for amphibious aircraft airborne equipment, the flight phase and region division process in S1 is as follows: Based on the typical mission profile of amphibious aircraft, the flight phases are divided into: land takeoff and climb, air cruise, descent, approach and landing, water landing, and water takeoff; the regional distribution of airborne equipment in the aircraft is divided into: radar compartment, cockpit, front electronic equipment compartment, through-cabin front equipment cabinet, through-cabin equipment cabinet, rear electronic equipment compartment, and system equipment compartment.

[0007] In the aforementioned method for constructing vibration test profiles for amphibious aircraft airborne equipment, S2 is specifically as follows: Before the flight test, measuring points were set up in the radar compartment, cockpit, front electronic equipment compartment, front equipment cabinet of the through compartment, through equipment cabinet of the through compartment, rear electronic equipment compartment and system equipment compartment, and vibration sensors were arranged at each measuring point; the flight test was carried out to collect measured vibration data in five flight phases, and five sets of measured vibration datasets were obtained.

[0008] In the aforementioned method for constructing vibration test profiles of amphibious aircraft airborne equipment, S3 is as follows: Time-domain and frequency-domain processing and analysis are performed on the measured vibration dataset, time-domain waveforms of data at each stage are plotted, and self-power spectral density analysis is performed; then the data is summarized, and the upper limit of the normal one-sided tolerance of the self-power spectral density under each flight stage is calculated.

[0009] In the aforementioned method for constructing vibration test profiles for amphibious aircraft airborne equipment, when performing self-power spectral density analysis, if periodic and random components exist, the periodic and random components need to be separated and processed separately.

[0010] In the aforementioned method for constructing a vibration test profile for amphibious aircraft airborne equipment, S4 is as follows: Based on the data processing results of S3, analyze the vibration conditions and vibration characteristics of each region of the aircraft, summarize and process the power spectral density spectrum to obtain the vibration test spectrum of the aircraft airborne equipment, and design the vibration test profile for amphibious aircraft airborne equipment by combining the analysis of typical mission profiles of the aircraft.

[0011] In the aforementioned method for constructing vibration test profiles for amphibious aircraft airborne equipment, the power spectral density analysis process is as follows: (1) Determine the analysis frequency; (2) Determine the required number of samples: Combine the datasets from each flight phase to form a data file; based on actual requirements, perform power spectrum estimation with a statistical accuracy of less than ±1dB at a 95% confidence level. To ensure accuracy, select a sample size of [number missing]. ; (3) Calculate the power spectral density: (a) Subsample the selected data segment to be processed. ,in: , NFFT is the length of the Fast Fourier Transform; (b) Add a Hanning window to each subsample; (c) Calculate the spectrum of each sample. :

[0012] In the formula, ; Indicates frequency as The amplitude at the value, N =NFFT, F s The sampling frequency of the original data; (d) Calculate the autopower spectral density of each sample. And corrected by the Hanning window coefficient:

[0013] The corrected result is:

[0014] (e) Piecewise average: The estimated value of the self-power spectral density is obtained by averaging across the total sample: .

[0015] In the aforementioned method for constructing vibration test profiles for amphibious aircraft airborne equipment, the process of separating periodic and random components is as follows: Suppose that the vibration signal passes through a bandpass filter with an amplification factor of 1, then we have:

[0016] In the formula, This represents the total mean square value of the filter output. Let be the mean square value of the random component. Let be the mean square value of the sinusoidal component. The power spectral density value of the random component. This represents the bandwidth of the filter; The vibration signals are respectively divided into bandwidths and Power spectrum analysis yields the following:

[0017] Solving for the given information, we get:

[0018]

[0019] and That is, the separated random component and sinusoidal component values.

[0020] Advantages of this invention: This invention divides the flight phases and areas where airborne equipment is located by analyzing typical mission profiles and vibration environments of amphibious aircraft. Then, it obtains measured vibration data through flight tests. Finally, it constructs a vibration test profile based on the analysis, processing, and summarization of the measured vibration data. This method addresses the problem that current main reliability vibration test profile construction methods are not very applicable to vibration tests of amphibious aircraft airborne equipment. It uses measured data to enhance the simulation of the actual use environment of the product in the in-field test, determining the vibration stress level and duration applied to different areas of airborne equipment during different flight phases. Based on the measured vibration stress obtained from flight tests, it solves the problem that constructing reliability vibration test profiles based on reference stress is not reasonable and effective, effectively improving the simulation effect of the in-field test on the actual use environment of the product. Furthermore, considering that GJB 150.16A does not currently have specific vibration test requirements for amphibious aircraft, this invention provides a feasible and effective method for constructing reliability vibration test profiles for large amphibious aircraft, solving the problem that existing main vibration test profile methods are not very applicable to amphibious aircraft. The method described in this invention is scientific, highly operable, and has great potential for widespread application. Attached Figure Description

[0021] Figure 1 This is a flowchart of the steps of the method of the present invention; Figure 2 This is a schematic diagram of the mission profile. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, 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.

[0023] The features and illustrative embodiments of various aspects of the present invention will now be described in detail. Numerous specific details are set forth in the following detailed description to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention may be practiced without requiring some of these specific details. The following description of embodiments is merely intended to provide a better understanding of the invention by illustrating examples of the invention. The invention is by no means limited to any specific setups and methods set forth below, but covers any improvements, substitutions, and modifications to structures, methods, and devices without departing from the spirit of the invention. Well-known structures and techniques are not shown in the drawings and the following description to avoid unnecessarily obscuring the invention.

[0024] It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other, and the various embodiments can be referenced and cited in each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0025] Example 1. A method for constructing a vibration test profile for airborne equipment of an amphibious aircraft, see [link to example]. Figures 1-2 Specifically, it includes the following steps: Step 1: Flight phases and area division for amphibious aircraft; Step 2: Collect measured vibration data of the aircraft; Step 3: Analysis, processing, and summarization of vibration measurement data; Step 4: Construct a reliability vibration test profile based on measured vibration data.

[0026] The specific process of the flight phase and area division described in step one is as follows: By analyzing typical mission profiles of amphibious aircraft, the flight phases are divided into five stages: land-based takeoff and climb, aerial cruise, descent, approach and landing, water landing, and water takeoff. Based on the distribution of onboard equipment and the airframe structural layout, the onboard equipment can be categorized into radar compartment, cockpit, forward electronics compartment, through-cabin forward equipment cabinet, through-cabin equipment cabinet, rear electronics compartment, and systems equipment compartment. This division of areas provides a reference for sensor placement in subsequent flight tests.

[0027] The specific process for collecting measured data in step two is as follows: To obtain measured vibration data and conduct flight tests, measuring points were set up at the locations described in Step 1: radar compartment, cockpit, forward electronic equipment compartment, forward equipment cabinet, through-cabin equipment cabinet, aft electronic equipment compartment, and system equipment compartment. Vibration sensors were deployed at each location. Through actual flight tests, measured vibration data were collected. Following the division of the flight phases in Step 1 into five stages—land takeoff and climb, air cruise, descent, approach and landing, water landing, and water takeoff—five sets of measured vibration data sets were obtained, each corresponding to one of the five flight stages. The acceleration unit for the measured data is g.

[0028] The specific process of vibration measurement data analysis, processing, and summarization in step three is as follows: The vibration measurement data after the data preprocessing in step two are then processed, including time-domain and frequency-domain processing and analysis, plotting the time-domain waveforms of each data segment, and performing power spectral density analysis. If periodic and random components exist, they need to be separated and processed separately. Then, the data is summarized, and the upper limit of the normal one-sided tolerance of the power spectral density under each flight stage is calculated (50% confidence level, 90% probability).

[0029] The specific process for constructing the reliability vibration test profile in step four is as follows: Based on the data processing results in step three, the vibration conditions and characteristics of different regions of the aircraft are analyzed, the power spectral density spectrum is summarized and processed, and then the vibration test conditions (i.e., vibration test spectrum) of the aircraft's airborne equipment are obtained. Combined with the analysis of typical mission profiles of the aircraft, the vibration test profile of the airborne equipment of the amphibious aircraft is designed.

[0030] This invention utilizes measured data to enhance the simulation of the actual use environment of the product in the indoor test, construct the correct test profile, and at the same time solve the problem that the current main reliability vibration test profile construction methods are not very applicable to vibration tests of amphibious aircraft airborne equipment.

[0031] Example 2. A method for constructing a vibration test profile for airborne equipment of an amphibious aircraft, see [link to example]. Figures 1-2 ,include: Step 1: Flight Phases and Area Division A typical mission profile diagram of an amphibious aircraft is shown below. Figure 2 As shown, by analyzing the typical mission profile of amphibious aircraft, the flight phases of the aircraft are divided into five stages: land take-off and climb, air cruise, descent, approach and landing, water landing, and water take-off.

[0032] Based on the distribution of airborne equipment and the aircraft's structural layout, the airborne equipment can be divided into the radar compartment, cockpit, forward electronics compartment, through-cabin forward equipment cabinet, through-cabin equipment cabinet, rear electronics compartment, and system equipment compartment. This division of areas provides a reference for sensor placement in subsequent flight tests.

[0033] Step 2: Collect measured data In order to obtain measured vibration data and conduct flight tests, measuring points were set up at the locations described in step one, including the radar compartment, cockpit, front electronic equipment compartment, front access equipment cabinet, access equipment cabinet, rear electronic equipment compartment, and system equipment compartment. Vibration sensors were then deployed at each location, and measured vibration data were collected through actual flight tests.

[0034] As described in Step 1, the flight phase is divided into five stages: land-based takeoff and climb, aerial cruise, descent, approach and landing, water landing, and water takeoff. This results in five sets of vibration measurement datasets, each corresponding to one of the five flight stages. The land-based takeoff and climb dataset contains 2.465 million data points per segment, with a duration of 308.2 seconds. The other four flight stage datasets each contain 4.93 million data points per segment, with a duration of 616.4 seconds. The measured acceleration is expressed in g, with a total of 200 data segments, a sampling frequency of 8000 Hz, and a sampling interval of 0.125 ms.

[0035] The dataset for the water takeoff phase includes conditions such as water skidding takeoff, landing on water, and go-around; the dataset for the water landing phase includes conditions such as approach, landing on water, taxiing, simulated taxiing takeoff, and taxiing takeoff.

[0036] Step 3: Analysis, processing, and summarization of vibration measurement data The vibration measurement data after the data preprocessing in step two are then processed. First, time-domain and frequency-domain processing and analysis are performed. The analysis results show that: (1) During the cruise phase in the air, the vibration amplitude of the cockpit is about 0.2g and the power spectrum is e-5g. 2 The vibration amplitude of the equipment cabinet before the cabin was opened was approximately 0.5g, with a power spectrum of e-5g. 2 The vibration amplitude of the through-cabin equipment cabinet is on the order of / Hz; the power spectrum is approximately 5g. 2 The amplitude of vibrations at the actuator, wing, and tail trailing edge is approximately 1g, with a power spectrum of e⁻⁵g. 2 On the order of / Hz.

[0037] (2) During the descent approach and landing phase, the vibration amplitude of the cockpit is about 1.5-2g, which is larger during landing and smaller during the descent phase (0.2g); the vibration amplitude of the equipment cabinet before the access cabin is about 4g, which is larger during landing and smaller during the descent phase (0.5g); the vibration amplitude of the equipment cabinet after the access cabin is about 6g, which is larger during landing and smaller during the descent phase (4g); the vibration amplitude of the actuators, wings and tail trailing edge is about 1.5g.

[0038] (3) During the water landing phase, the vibration amplitude of the cockpit is less than 1.5-2g, and the amplitude changes significantly with each landing; the vibration amplitude of the equipment cabinet before the cabin is about 1.5g, with a maximum value of about 2g; the vibration amplitude of the equipment cabinet after the cabin is about 6g, with a maximum value of about 10g; the vibration amplitude of the actuator, wing, and tail trailing edge is about 2g, and the change is not significant with each landing.

[0039] (4) During the takeoff and climb phase on land, the vibration amplitude of the cockpit is about 1g, which is larger during takeoff and smaller during climb (0.25g); the vibration amplitude of the equipment cabinet in front of the cabin is about 3g, which is larger during takeoff and smaller during climb (1g); the vibration amplitude of the equipment cabinet in the cabin is about 10g, which is larger during takeoff and smaller during climb (8g), with the vertical amplitude being smaller than the lateral amplitude; the vibration amplitude of the actuators, wings, and tail trailing edge is about 2g, with no significant change in amplitude during takeoff and climb.

[0040] (5) During the takeoff phase on water, the vibration amplitude of the cockpit is about 0.6g. The amplitude changes significantly with each maneuver, and the climb and descent are relatively small (0.2g). The vibration amplitude of the equipment cabinet before the cabin is about 1.5g. The amplitude changes significantly with each maneuver, and the climb and descent are relatively small (0.5g). The vibration amplitude of the equipment cabinet after the cabin is about 8g. The amplitude changes significantly with each maneuver, and the climb and descent are relatively small (3g). The vibration amplitude of the actuators, wings, and tail trailing edge is about 2g. The amplitude changes are not significant during takeoff and climb.

[0041] After frequency domain analysis, the processed signal is subjected to autopower spectral density analysis to obtain the autopower spectral density values ​​of each measurement point under each flight phase, and vibration power spectrum graphs of each measurement point in each flight phase are plotted. The specific steps are as follows: (1) Determine the analysis frequency. The original data sampling frequency is 8000Hz, the sampling interval is 0.125ms, and the analysis frequency is 20-2000Hz; (2) Determine the required number of samples. Combine the datasets from each flight phase to form a data file. Based on actual requirements, perform power spectrum estimation with a statistical accuracy of less than ±1 dB at a 95% confidence level. To ensure accuracy, select a sample size of [number missing]. .

[0042] (3) Calculate the power spectral density.

[0043] (a) Select the data segment to be processed, and perform subsampling with NFFT=8192. NFFT is the length of the Fast Fourier Transform, where: ;

[0044] (b) Add a Hanning window to each subsample; (c) Calculate the spectrum of each sample.

[0045]

[0046] In the formula, ; Indicates frequency as The amplitude at the value; N =NFFT, F s The sampling frequency of the original data; (d) Calculate the autopower spectral density of each sample. And corrected by the Hanning window coefficient;

[0047] The corrected result is:

[0048] (e) Piecewise average The estimated value of the self-power spectral density is obtained by averaging across the total sample:

[0049] Then, periodic data separation processing is performed. When performing self-power spectral density analysis on the vibration signal using the self-power spectral density test method, if a peak appears at a certain frequency, it may contain a sinusoidal signal at that frequency. However, narrowband random components generated by the resonance of a small-damped structure may also exhibit peaks, so it is necessary to separate the sinusoidal components and the narrowband random components.

[0050] Suppose the vibration signal contains sinusoidal and random components, and the power spectral density of the random component remains constant within a certain local frequency band. Assuming it passes through a bandpass filter with bandwidth B and amplification factor of 1, then:

[0051] In the formula, This represents the total mean square value of the filter output. Let be the mean square value of the random component. Let be the mean square value of the sinusoidal component. The power spectral density value of the random component. This represents the bandwidth of the filter.

[0052] The vibration signals are respectively divided into bandwidths and Power spectrum analysis yields the following:

[0053] because and It is known that and It can be measured from the power spectrum, and the solution can be obtained as follows:

[0054]

[0055] and These are the separated random and sinusoidal component values. Based on the above method, sinusoidal signals were extracted from the vibration data during the air cruise, takeoff (on land), and climb (after takeoff from land) phases. The results are shown in Table 1.

[0056] Table 1. Calculation results of sinusoidal components at each stage

[0057] Then, the data is summarized, and the upper limit of the normal one-sided tolerance of the self-power spectral density under each flight stage is calculated (50% confidence level and 90% probability).

[0058] Step 4: Constructing a reliability vibration test profile Based on the data processing results in step three, we can summarize and conclude that: (1) The vibration value of the through cabin is much higher than that of other cabins, and it is not appropriate to summarize it together with other cabins. Therefore, the vibration conditions should be divided into two parts: through cabin vibration conditions and other cabin vibration conditions.

[0059] (2) The vibration characteristics of the takeoff and landing segments in each flight mission are similar, and the power spectral density is basically the same, so they can be summarized as the same power spectral density. The vibration characteristics of water takeoff and water landing (water) are similar to those of land takeoff and landing segments, and the magnitudes are not much different, so they can be summarized as the same power spectral density.

[0060] (3) The climbing, descending and cruising segments are quite similar, and their power spectrum vibration spectrum shapes are similar. The vibration values ​​of the climbing and descending segments are slightly higher than those of the cruising segment. They can be summarized as a power spectral density spectrum shape, but the magnitudes are different.

[0061] (4) The shape of the power spectral density of the takeoff and landing phase is different from that of the climb, descent and cruise phases during flight. In order to facilitate the implementation of the test, the vibration conditions of other cabins except the through cabin were engineered and summarized into the same power spectral density shape, but with different magnitudes.

[0062] (5) The extracted sinusoidal vibration values ​​are relatively small. To facilitate the implementation of the experiment, a narrow-band random method is used for induction processing.

[0063] Based on the above summary and data processing results, the vibration test conditions for the airborne equipment of amphibious aircraft can be obtained, which are divided into through-cabin and non-through-cabin areas. The vibration test conditions are shown in Table 2 and Table 3.

[0064] Table 2 Vibration Test Conditions (Open Chamber)

[0065] Table 3 Vibration Test Conditions (Other Chambers) .

[0066] The above-described embodiments merely illustrate the implementation methods of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A method for constructing a vibration test profile for airborne equipment of an amphibious aircraft, characterized in that, include: S1. Flight phases and area divisions for amphibious aircraft: Based on the typical mission profile of amphibious aircraft, the flight phases are divided into: land takeoff and climb, air cruise, descent, approach and landing, water landing, and water takeoff; the regional distribution of airborne equipment in the aircraft is divided into: radar compartment, cockpit, front electronic equipment compartment, through-cabin front equipment cabinet, through-cabin equipment cabinet, rear electronic equipment compartment and system equipment compartment. S2. Collect measured vibration data of the aircraft; S3. Analysis, processing, and summarization of measured vibration data: The measured vibration dataset was processed and analyzed in the time and frequency domains, and the time-domain waveforms of the data at each stage were plotted. The self-power spectral density was then analyzed. The data was then summarized, and the upper limit of the one-sided tolerance of the normal distribution of the self-power spectral density at each flight stage was calculated. When performing power spectral density analysis, if periodic and random components exist, they need to be separated and processed separately. The separation process is as follows: Suppose that the vibration signal passes through a bandpass filter with an amplification factor of 1, then we have: ， In the formula, This represents the total mean square value of the filter output. Let be the mean square value of the random component. Let be the mean square value of the sinusoidal component. The power spectral density value of the random component. This represents the bandwidth of the filter; The vibration signal is divided into bandwidths. and Power spectrum analysis yields the following: ， Solving for the given information, we get: ， ， and That is, the separated random component and sinusoidal component values; S4. Construct a reliability vibration test profile based on measured vibration data.

2. The method for constructing vibration test profiles for amphibious aircraft airborne equipment according to claim 1, characterized in that: S2 is as follows: Before the flight test, measuring points were set up in the radar compartment, cockpit, front electronic equipment compartment, front equipment cabinet of the through compartment, through equipment cabinet of the through compartment, rear electronic equipment compartment and system equipment compartment, and vibration sensors were arranged at each measuring point; the flight test was carried out to collect measured vibration data in five flight phases, and five sets of measured vibration datasets were obtained.

3. The method for constructing vibration test profiles for amphibious aircraft airborne equipment according to claim 1, characterized in that: S4 is as follows: Based on the data processing results of S3, analyze the vibration conditions and vibration characteristics of each region of the aircraft, summarize and process the power spectral density spectrum to obtain the vibration test spectrum of the aircraft's airborne equipment, and design the vibration test profile of the amphibious aircraft's airborne equipment by combining the analysis of typical mission profiles of the aircraft.

4. The method for constructing vibration test profiles for amphibious aircraft airborne equipment according to claim 1, characterized in that: The power spectral density analysis process is as follows: (1) Determine the analysis frequency; (2) Determine the required number of samples: Combine the datasets from each flight phase to form a data file; based on actual requirements, perform power spectrum estimation with a statistical accuracy of less than ±1dB at a 95% confidence level. To ensure accuracy, select a sample size of [number missing]. ; (3) Calculate the power spectral density: (a) Subsample the selected data segment to be processed. ,in: , NFFT is the length of the Fast Fourier Transform; (b) Add a Hanning window to each subsample; (c) Calculate the spectrum of each sample. : ， In the formula, ; Indicates frequency as The magnitude at the value, N=NFFT, F s The sampling frequency of the original data; (d) Calculate the autopower spectral density of each sample. And corrected by the Hanning window coefficient: ， The corrected result is: ， (e) Piecewise average: The estimated value of the self-power spectral density is obtained by averaging across the total sample: 。

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