Basic concepts of Signal Processing

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Sensor Type:The sensor can be divided into different types according to the different working modes of each component of the sensor. The relative and absolute (Inertial) types can be divided according to different receiving methods; there are two types, generator type and parameter type, based on the difference of the electromechanical conversion output. The measurement circuit outputs different link characteristics to meet different test requirements. Such as displacement (GAP) voltage characteristics, speed voltage characteristics, acceleration voltage characteristics and so on. The relative receiving method refers to a working method that uses the sensor housing as the reference coordinate to directly receive mechanical vibration by means of the change of the pin or gap. The result is the relative vibration value of the shell as the reference coordinate. The inertia receiving method receives the vibration momentum measured through the spring single degree of freedom vibration system. When working, its shell is fixed on the vibrating object, and the entire sensor (including the mass block) vibration follows the vibration of the object, but the electromechanical conversion link --- the coil is fixed on the shell with a very soft spring, its self-vibration frequency is much lower than the vibration frequency of the vibration body, so it is relatively static for the vibration body, in other words, the coil is fixed, is an absolute reference coordinate system, so the measured result is an absolute vibration value. The inertial reception method is also called seismic. Performance indicators of Sensors Sensitivity:It refers to the voltage signal output value u that can be obtained by inputting X to the unit vibration volume along the measurement axis of the sensor. That is, one metric related to the sensitivity of S = u/X is the resolution, this is the minimum mechanical vibration input variation △x that can be identified by output voltage variation △u. To measure small vibration changes, the sensor should have a high sensitivity. Frequency Range:The value of the sensitivity that changes with the frequency does not exceed the frequency range of the given error. The two ends are the lower frequency limit and the upper limit. To measure the static mechanical volume, the sensor should have zero-frequency response characteristics. In addition to the frequency response characteristics of the sensor, the frequency range of the sensor is also related to the sensor installation conditions (mainly affecting the upper limit of the frequency ). Dynamic Range:The range that can be measured in the dynamic range is the amplitude range of the input mechanical volume whose sensitivity changes with the amplitude does not exceed the given error limit. In this range, the output voltage is proportional to the mechanical input, so it is also called a linear range. Generally, the dynamic range is expressed in decibels rather than absolute values. This is because the amplitude of the measured vibration value is too large, and it is more convenient to use it in decibels. Phase Shift:It refers to the phase lag of the relative input of the same frequency voltage signal when the input is simple harmonic vibration. The existence of the phase shifting may cause the output waveform to change in size. To avoid output distortion, the phase shifting value must be zero or varying, or change in proportion to the frequency. Environment conditions:Including requirements for operating temperature, ambient temperature, electromagnetic field shielding, etc. The following table summarizes the characteristics and advantages and disadvantages of the m3000 system vibration sensor: Sampling and quantization error:The process of analog signal discrete sampling (A/D) conversion, including sampling, quantization, encoding, and so on. Signal Sampling:Sampling, also known as sampling, refers to the discretization of signals in time, that is, the instantaneous value of △t at a certain interval on the analog signal x (t) point by point. It is achieved by multiplying the sample pulse and the analog signal. Quantification:Is to discretization the amplitude, that is, the vibration amplitude is expressed by the binary quantization level. The quantitative level changes according to the series, and the actual vibration value is a continuous physical quantity. The specific vibration value is rounded down to the near quantization level. Sample interval selection and signal obfuscation:The sampling interval must be determined before sampling analog signals. Reasonable Selection of △t involves many technical factors that need to be considered. Generally, the higher the sampling frequency, the closer the sampling points are, and the closer the obtained discrete signal is to the original signal. However, an excessively high sampling frequency is not desirable. For signals with a fixed length (t), a large amount of data (n = T/△t) is collected ), increase unnecessary computing workload and storage space for the computer. If the data volume (n) is limited, the sampling time is too short, leading to the exclusion of some data information. If the sampling frequency is too low and the sampling interval is too long, the discrete signal is insufficient to reflect the waveform characteristics of the original signal, and the signal cannot be restored, resulting in signal confusion. Intuitively speaking, signal mixing is to mistake a high-frequency signal for a low-frequency signal ,... In order to deepen our understanding of signal obfuscation, we will explain it from the spectrum perspective. The signal mixing of Time-domain waveforms is reflected in the spectrum called frequency mixing. Frequency Mixing is a special term in the signal technology. It refers to the confusion between high and low frequencies in the frequency domain due to the improper selection of sampling time intervals in the time domain, it is also called Fold distortion. To understand the essence of frequency mixing, we need to understand Discrete Fourier transformation. Discrete Fourier transformation is transformed from the Fourier transformation of an infinite continuous signal. Because computers can only operate and store discrete sequences with limited lengths, they must perform discrete sampling and truncation for Continuous Time-domain signals and continuous spectrum, which is the origin of Discrete Fourier transformation. A reasonable sampling interval should be that it will not cause signal confusion and will not increase the computer's workload too much. The sampling theorem proves that the minimum sampling frequency fs without frequency mixing should be twice the highest frequency FM in the signal, that is, FS ≥2fm. Considering the requirements of the binary representation of the computer, generally, FS = (2.56 ~ 4) FM. Anti-mixed Filtering:It should be noted that the sampling theorem only ensures that the signal is not distorted into a low-frequency signal, but cannot be guaranteed not to be disturbed by the high-frequency signal, if the signal output by the sensor contains a frequency component higher than the required signal frequency, the/D board will sample the component at the selected sampling frequency and mix it into the useful signal (although not the original form of noise, it is only the distorted energy, but also the interference to the real information .) Therefore, before sampling, filter out the frequency components that are higher than the desired signal, which is anti-mixed filtering. Otherwise, the components cannot be distinguished after sampling.

Sample Length selection and frequency resolution:The sample length is the length of the sample time. During sampling, we must first ensure that the overall picture of the signal can be reflected, and the transient signal should include the entire transient process. For the periodic signal, we can collect a periodic signal theoretically. In fact, considering the average signal requirement and other factors, sampling always has a certain length. In order to reduce the calculation amount, the sampling length should not be too long. A sufficient length is required for signal sampling. This is not only to ensure the integrity of the signal, but also to ensure a good frequency resolution. If the analysis frequency is set to FC and the number of spectral lines is N, then the frequency resolution is △f = FC/N and the sampling frequency is used for representation, △f = FS/2.56n = 1/△t/2.56n = 1/n
In the △t = 1/T formula, the number of sampling points is the sample length. It can be seen that, for a given analysis frequency, the larger the sample length (t), the smaller the △f, that is, the higher the Resolution, the visible frequency resolution is inversely proportional to the sample length. In signal analysis, the number of sampling points n is generally set to a multiple of 2 m, and more than 512, 1024, 2048, and 4096 are used.Signal truncation:The computer can only analyze discrete data with a limited length (such as 1024 points) at a time. That is to say, the original continuous time-domain signal must be truncated into several fixed-length signals, then, the computer analyzes the intercepted signal segment.Leakage:Truncation affects the accuracy of spectral analysis. If the time-domain signal is periodic, And the truncation is based on the number of the whole cycle, the signal truncation will not cause problems, because each cycle signal can represent the change of the entire cycle signal. If the data is not captured in the whole cycle, the truncation will cause a mutation at both ends of the signal waveform. The intercepted signal is very different from the original signal. When the time-domain signal is analyzed, originally, the concentrated linear spectrum will be scattered in the adjacent frequency band to generate a new frequency component that does not exist in the original signal. In the spectrum analysis technology, this effect is called a leak. This means that the original concentrated frequency information is leaked to the next frequency band, which affects the accuracy of spectral analysis and interferes with the recognition of spectrum. If the time-domain signal is a random signal, the truncation result will show wrinkles on the original continuous spectrum, that is, the wrinkle effect, will also affect the recognition of the spectrum. Signal truncation causes leakage due to signal distortion. Because truncation is equivalent to multiplying a rectangle window function and a signal, according to the convolution theorem, the spectrum is the convolution of two time Function Spectra, that is, the spectrum is multiplied at the corresponding frequency, because the spectrum of the rectangle function is an infinite bandwidth spectrum with a side lobe (the image corresponding to the fundamental frequency is called the main lobe, and the side lobe is called the harmonic frequency ), therefore, the spectral lines are extended into the shape of the rectangular signal spectrum window (sin (wt) function. In order to reduce the leakage error, in addition to the entire cycle truncation, the main method is to add a window.

 

Add window:The dominant idea of window addition is to use a relatively smooth window function instead of the rectangular window function for intercepting the signal sample, that is, to carry out specific unequal weighting on the truncated time series signal, the abrupt changes at both ends of the truncated waveform become smoother to reduce the side-lobe of the spectrum window. Because of the maximum number of side-lobe leaks, the number of side-lobe leaks is also reduced. There are many window functions used for signal processing, which are commonly used in engineering, such as rectangular windows, Hanning windows, hanming windows, and Cosine windows. The characteristics of various windows are described as follows: l rectangular windows are characterized by a narrow main flap, however, the side lobe is large, especially when the first side lobe is too high, which is 21% of the main side, so the leakage is very large. L Hanning window (Hanning), with a very small side lobe and rapid attenuation. The main lobe is wider than the main lobe of the rectangular window, and the leakage is much smaller than that of the rectangular window. L Hamming window (Hamming) is made up of rectangular window and Hanning window. The first side lobe is very small, and the other side lobe attenuation is slower than that of Hanning window. The main lobe width is between the rectangular window and Hanning window. L The Gaussian bell-shaped window has only the primary valve without a side lobe. The width of the primary valve is too large and its shape is adjustable. To reduce leakage, the Gaussian window should be thinner. L The cosine window main lobe is triangular, and the side lobe is very small. Regarding the selection of window functions, the nature and processing requirements of the analyzed signals should be considered. If only the accuracy is required to read the frequency of the main flap without considering the amplitude accuracy, you can choose a rectangular window with narrow width and easy resolution, such as measuring the natural vibration frequency of an object. If the narrow band signal is analyzed, if there is strong interference noise, select a window function with a small amplitude of the Side-lobe, such as Hanning window and triangular window.Sampling Method:The sampling method can be equi-time interval △t and equi-angular displacement △phi. Generally, the same interval sampling method is used, that is, fixed sampling frequency sampling. This method is easy to achieve, without the need for key-Phase Signal combination, for stable speed signal, this method can obtain a good signal. However, it is not good to collect the unit Speed Fluctuation Signal (such as the ascending and descending speed signal). First, it is possible that the sampling frequency fs cannot meet the requirements of the sampling theorem because it cannot keep up with the speed change, signal Distortion. Second, the signal is no longer cyclical due to the speed change. The spectrum becomes a continuous spectrum, and the discrete spectral lines become the spectral band or the spectral lines become fat, especially the higher-order harmonic, the bandwidth changes proportionally according to order, and the spectral band is wider, and the spectral diagram becomes blurred and difficult to distinguish. Because the signal power is scattered on a series of spectral lines, in addition to the large deviation of the amplitude, the details of the Side-lobe structure are sometimes drowned, this is detrimental to unit failure analysis. For example, the sampling frequency can be changed to synchronize the change with the rotation speed, then, the rotation speed frequency shown on the spectrum and its various harmonic waves will clearly maintain the relationship between them, and the blur of the line can be eliminated. Synchronous sampling is triggered at the same angle to ensure that the number of sampling points is the same every week, which is equivalent to the periodic nature of the signal, so as to obtain a clear order spectrum.False alarm:There are many reasons for false alarms. One is that the sensor fails to work in harsh environments for a long time, the other is that the sensor is improperly installed or is loose and damaged after long-term operation, and the third is that the sensor is magnetized, frequent signal cable insulation loss, Secondary Instrument wire looseness or grounding is also the cause of false alarm.Signal-to-noise ratio:In the acquired signal, interference components are always mixed. This is called noise. The noise is too large and the useful signal is not prominent, so it is difficult to make accurate analysis. Technically, the signal-to-noise ratio is measured by signal-to-noise ratio, expressed by the symbol S/N. Before performing Signal Analysis, try to reduce the impact of noise interference. Increasing the number of S/N is a major part of signal processing.Improve signal-to-noise ratio:The main ways to increase s/n are Time Domain Average and filtering.Filter:The main purpose of filtering is to try to separate noise from useful signals and suppress and eliminate them. There are two filtering methods: analog filtering and digital filtering, there are four basic types: low-pass, high-pass, and band-resistance. The functions of various filters are shown in the following table:Simulated Filtering:The filtering method implemented by the analog circuit first uses a simulated filter before sampling, which can improve the signal quality and reduce the workload and difficulties of subsequent data processing, such as the Anti-mixing filter in the signal regulator das100.Digital Filtering:The essence of digital filtering is to calculate the acquired discrete data, enhance or enhance the signal required, reduce or filter out the interference components, and apply linear and non-linear filtering to digital filtering, linear filtering is applicable to linear superposition of useful signals and noise, while nonlinear filtering is applicable to multiplication (such as Amplitude Modulation) and convolution (such as impact-induced Transfer Response. Convolution can be converted into a product relationship through Fourier transformation, while Multiplication can be converted into an addition relationship through logarithm. Therefore, nonlinear filtering can be converted into linear filtering.Image range processing:As a measure of the vibration intensity, the vibration amplitude is the most basic data for equipment fault diagnosis. The displacement peak-peak XP-P reflects the vibration displacement dual amplitude, which is mainly used to determine the relationship between the vibration size and the matching gap. The vibration speed value is Vrms, which reflects the vibration energy and is a parameter used to determine the vibration intensity. The simple amplitude parameter is only a measure of the device's actual vibration. Its value is related to both the fault and the working conditions (load, speed, and instrument sensitivity, in fact, the development of fault discovery cannot be achieved from its magnitude. Therefore, the simple range parameter can only be used for vibration evaluation reference and is not sensitive to fault reflection. Non-dimensional amplitude parameters: waveform indicators (shape factor) Sf = xrms/ABS (x) peak indicators (crest factor) Sf = xmax/xrms pulse indicators (impulse factor) if = xmax/ABS (x) margin indicator (clearance factor) CLF = xmax/XR kurtosis indicator (kurtosis value) KV = beta/xrms among the above categories, xrms, ABS (x), xmax, xr, and beta are vibration valid values, absolute average value, maximum value, Gini amplitude, and kurtosis, respectively. The numerator of the above parameters is the maximum vibration value or the high power of the vibration, which highlights the large amplitude, which is essentially an increase in the large amplitude. At the same time, the stable vibration value that is basically adapted to the running condition of the unit is selected as the reference value, so as to eliminate the influence of the vibration on parameters under the working condition and improve the fault sensitivity. Among these parameters, the kurtosis, margin, and pulse indicators are sensitive to impact Faults, especially when faults occur in the early stages; however, when the fault develops to a certain extent, it decreases, indicating that they are highly sensitive to early faults, but have poor stability. Generally speaking, the root-mean-square value is stable but not sensitive to early failure signals. Therefore, to achieve better results, we need to apply them at the same time to ensure both sensitivity and stability.Time Domain Transformation:Data is transformed in chronological order. There are two situations: Self-correlation function transformation and cross-correlation function transformation.Auto-related functions:The purpose of auto-correlation function transformation is to understand the dependency or similarity between the vibration at a time point and the vibration at another time point. It is expressed by the average value of the product of the vibration at two time points. That is, the auto-correlation function can be used to check whether the data is related. Secondly, it can be used to test the periodic signals mixed in random noise. Normal machines have no faults and the vibration is random. Therefore, the auto-correlation function is a narrow pulse. When a fault occurs, especially when a periodic shock occurs, the time delay is an integer multiple of the cycle, and the self-correlation function will have a large peak value.Mutual function:Similar to the auto-correlation function, the cross-correlation function is used to represent the dependencies between two groups of data in chronological order. It is also expressed by the average value of the product of the two vibration values at different time points, only the product value comes from two different groups of data. The cross-correlation function can determine the position of the signal source. Due to the delay of signal transmission in the channel, the time delay of the cross-correlation function peak value can be determined, in addition, the auto-correlation function can detect the Periodic Signal disturbed by channel noise.Frequency Domain conversion:The complex time signal is transformed into a structure represented by a frequency component. Frequency-domain conversion is the most widely used processing method in mechanical equipment fault diagnosis. Because of faults, the signal frequency structure changes often during development, many fault causes can be explained and elaborated.Spectrum:In the form of Cartesian coordinates, the frequency domain transformation is a commonly used spectral chart. Spectrum is a general term. The specific content of video rate components include amplitude spectrum, phase spectrum, power spectrum, energy spectrum, and inverted spectrum. The Mathematical Principle of spectrum transformation is Fourier transformation. For periodic signals, this illumination can be implemented through Fourier series to obtain the discrete amplitude spectrum. for transient signals, the continuous spectrum can be obtained through Fourier points, which corresponds to the discrete spectrum, the continuous spectrum value is switched to the spectral density concept.Power spectral density function:The spectrum obtained by Fourier transformation of the time average signal square. It indicates the distribution of vibration power with frequency.Inverted spectrum:The inverted spectrum is a new technology in modern signal processing technology. It can analyze the periodic structure of complex spectrum charts and separate and extract the Periodic Components in intensive frequency modulation signals. It is very effective for analyzing complex signals such as homophone or cross-family harmonic frequencies and multi-component edge frequencies. The inverted spectrum transformation is the re-transformation of the Fourier Integral Transformation of the frequency-domain signal. The time-domain signal x (t) can be converted to the frequency Function x (t) or the power spectrum density function GX (f) After Fourier Integral Transformation ), if the spectrum diagram shows a complex periodic structure and is difficult to distinguish, the logarithm of the power spectrum density is then transformed by Fourier Integral, the periodic structure can be concentrated in a line form that is easy to identify. The square of the second Fourier transformation is the inverted power spectrum CP (Q) of x (t). Its Expression is CP (q) = ABS {f [loggx (f)]}. 2. It is expressed in words that the inverted power spectrum is the "logarithm power spectrum". The open side of the inverted power spectrum is CC (q) = SQRT [Cp (q)]. = ABS {f [loggx (f)]} refers to the amplitude inverted spectrum, or the inverted spectrum. In this formula, the variable is called the inverted spectrum, and its dimension is time. Generally, the Q unit is ms. A high Q value is called a low inverted frequency, indicating fast fluctuations and intensive harmonic frequencies on the spectrum. A low Q is called a low inverted frequency, indicating slow fluctuations and discrete harmonic frequencies on the spectrum.Fourier analysis:Fourier analysis is a mathematical method for dividing a source signal into a sine wave of different frequencies, or converting a time-domain signal into a frequency-domain signal. However, FFT analysis has serious defects. First, the time information is lost when the time-domain signal is converted to the frequency-domain signal, so that we cannot see the time when the event occurred when observing the frequency-domain diagram. In addition, FFT is based on the assumption that the signal is stable, so strictly speaking, FFT is only applicable to the analysis of the stable signal. Secondly, the essence of FFT analysis is a linear transformation method. In the case of a large rotating machine failure, it will show a strong non-linear nature. At this time, FFT analysis is used to process them. Short-term Fourier Transformation: Short-term Fourier Transformation (STFT), also known as window addition Fourier transformation, is to multiply the signal by a Sliding Window Function and then perform Fourier transformation on the signal H (t-tao) in the window. Its definition is: stftf (W, Tao) = f (t) H * (t-tao) E-jwtdt in the integral formula between positive and negative infinity, * indicates the complex concatenation, h (t) window functions such as Hamming, Hanning, and Gabor can be used to obtain the "local" spectrum of a group of original signals along with the movement of Tau, so as to reflect the time-frequency distribution characteristics of non-stable signals. From the formula, we can see that STFT has the time domain localization function. h (T-tao) is a sliding window in the time domain, which is equivalent to a band-pass filter in the frequency domain. STFT can analyze non-stable dynamic signals, because it is based on Fourier transformation, it is more suitable for analyzing quasi-stable signals. In STFT calculation, when h (t) is selected, the time-frequency resolution remains unchanged, STFT lacks the ability to refine, reflecting the non-stable features of strong transient signals. STFT provides a method to observe signals in both the time and frequency domains. However, because the length of the sliding window is fixed for all frequency components, STFT can only ensure limited accuracy, it still has a large error in analyzing transient signals with dramatic changes.Concept of white noise:White Noise refers to the noise in which the power spectral density function is constant, or the distribution of power evenly in the frequency domain. "White" refers to the concept of spectroscopy, because white light is a composite light, including all wavelengths of light. White Noise is only an idealized concept. If the noise power spectral density function is constant only within a certain frequency range, the system bandwidth to be considered is within this frequency range and far smaller than this frequency range. At this time, the noise can be processed as white noise. When it comes to Gaussian noise, it is often used together with white noise. However, they are two different concepts. Gaussian noise refers to the noise in which the probability density of the voltage or current amplitude conforms to the Gaussian distribution (I .e. normal distribution. Gaussian noise and white noise are defined from different angles. There is no inevitable relationship between them. Gaussian noise is not necessarily white noise, and vice versa. If it is both Gaussian noise and white noise, it is called "Gaussian white noise ". Gaussian white noise is a typical type of noise. It is often used as an ideal noise model in signal or system noise analysis and noise signal detection.Analysis Frequency/sampling points/number of spectral lines setting points
1. Maximum analysis frequency: FM refers to the highest analysis frequency and the highest signal frequency after anti-mixed filtering. According to the sampling theorem, the relationship between the FM and the sampling frequency fs is generally: FS = 2.56fm, and the selection of the highest analysis frequency depends on the device speed and the expected fault nature. 2. The relationship between the number of sampling points n and the number of spectral lines m is as follows: n = 2.56 m The relationship between the number of spectral lines m and the frequency resolution △f and the highest analysis frequency FM is as follows: △f = FM/m That is, M = FM/△f So: N = 2.56fm/△f
★The number of sampling points depends on the required frequency resolution. For example, if the machine speed is r/min = 50Hz and the fault frequency to be analyzed is estimated to be less than 8 times, the frequency resolution must be 1Hz for the spectrum, set the sampling frequency and number of sampling points to: Maximum analysis frequency fm = 8 · 50Hz = 400Hz;Sampling frequency fs = 2.56 · fm = 2.56 · 400hz = 1024Hz;
Sample Points n = 2.56 · (FM/△f) = 2.56 · (400Hz/1Hz) = 1024 = 210
Number of spectral lines M = N/2.56 = 1024/2. 56 = 400
According to the FFT transformation, we actually get the 1024-point line, but we know that there is a negative frequency in the mathematical computation, which is symmetric. Therefore, in fact, we are concerned with the line corresponding to the positive frequency, that is to say, the positive frequency has a 512 line. Why do we usually say this is a 400 line, it is generally believed that the spectrum accuracy between the 401-512 lines is not high due to the influence of frequency mixing and time domain truncation.Selection of Vibration SensorsVibration sensors are divided by working principle, including eddy current, speed, acceleration, capacitance, and inductance. The latter two types are rarely used because they are greatly affected by the surrounding media. Reasonable Selection of vibration sensors in unit vibration measurement can not only obtain satisfactory measurement results, save labor and time, but also identify the cause of vibration failure as soon as possible, it plays an important role in improving the accuracy of rotor balancing and reducing the number of times the unit starts and stops. Reasonable Selection of sensors mainly involves two aspects: first, sensor performance; second, conditions and requirements of the objects to be tested. Only a good combination of the two can achieve the best results. For measuring the vibration of a steam turbine generator set, both the eddy current sensor and the speed sensor are required. However, in general testing, due to the trouble of installing the eddy current sensor, the requirements are strict and time-consuming, so we try our best to replace it with a speed sensor. However, in some Vibration Fault Diagnosis and when the ratio of rotor quality to stator quality is less than 1/10, such as the high-pressure part of the turbine, the eddy current sensor should be used to measure the vibration of the shaft. On the contrary, when the ratio of rotor mass to stator mass is large, such as the Turbine Low Voltage and generator part, the speed sensor should be used to measure the bearing vibration or the absolute vibration of the rotating shaft. In order to have a brief understanding of the performance of the above three kinds of vibration sensors, the main characteristics and advantages and disadvantages of these sensors are summarized as follows for reference during the selection. (1)             Advantages of eddy current sensor: 1. it can directly measure the vibration of the rotating shaft and perform static and dynamic measurements. It is suitable for the environmental conditions of most machines. 2. the output signal is proportional to the vibration displacement. For most machines that use amplitude to describe the vibration state, it can obtain a high output signal.
3. the structure is simple and the size is small. It has an appropriate frequency range for the vibration of the Steam Turbine Generator Set and is easy to calibrate (verify.
4. In addition to measuring the static position of the vibration and components, you can also measure the center position of the shaft, the moving track of the center of the shaft during startup, and the change of the center of the bearing. In addition, it can be used as the key phase signal for speed measurement and vibration phase measurement. Disadvantages: 1. When the measurement of vibration object materials is different, the linear range and sensitivity of the sensor need to be re-calibrated. 2. the power supply is required, which is difficult to install and has strict requirements and must be equipped with a front-end device.
(2) Speed Sensor
Advantages:
1. simple installation, applicable to the environment conditions of a large number of machines.
2. There is no need for power supply, and the vibration signal can be transmitted to the desired place without any processing.
3. The movable parts are vulnerable to damage and the low-frequency response is poor. Generally, a speed sensor below 15Hz will produce a large amplitude and phase error, which affects the complete message at 3 × ω N (ω n is the natural vibration frequency of the sensor .)Note: At present, some manufacturers have developed low-frequency speed sensors, which can measure 0.5 ~ 60Hz. (3) AccelerometerSmall size, light weight. It can be applied to some vibration testing systems that are greatly affected by the attached quality, but its installation method and wire laying method have a great impact on the measurement results. for Steam Turbine Generators, its working frequency range is too high and it is difficult to calibrate.Power Spectrum: What are the differences and connections between spectrum and power spectrum? Spectrum is a very non-strict concept. It often refers to the Fourier transformation of the signal, which is a time average) the concept of power spectrum is aimed at limited power signals (Available Energy Spectrum Analysis of limited energy signals). It represents the conversion of signal power with frequency in a unit band. The amplitude information of the spectrum is retained, but the phase information is lost. Therefore, the power spectrum of different spectrum signals may be the same. There are two important differences: 1. The power spectrum is the statistical mean concept of a random process. The power spectrum of a stable random process is a definite function, while the spectrum is the Fourier transformation of samples in a random process. For a random process, the spectrum is also a "random process ". (Random frequency series) 2. The difference between power concept and amplitude concept. In addition, only the power spectrum can be discussed for the second-order moment process of the wide and steady state. The existence of the power spectrum depends on whether the second-order moment exists and the Fourier transformation of the second-order moment converges; the existence of the spectrum only depends on whether the Fourier transformation of the sample in the random process converges.What is power spectrum? Does it have a unit?Random Signals are infinite signals in the time domain and do not have integral conditions. Therefore, it is not possible to directly perform a Fourier transformation. The power spectrum with statistical characteristics is generally used as the basis for spectral analysis. The power spectrum and auto-correlation function are a Fourier transformation pair. The power spectrum has an average power dimension per unit frequency. Therefore, the standard definition is the power spectral density. The power spectral density function shows the distribution of random signal energy with frequency. The white noise is a straight line above the W axis parallel to the W axis. The power spectral density, in terms of name decomposition, means that the observed object is the power, the observed domain is the spectral domain, usually the frequency domain, and the density refers to the distribution of the observed object in the observed domain. In general, the power spectral density we talk about is for the stable random process. Because the sample function of the stable random process is generally not absolutely product-able, we cannot directly perform Fourier analysis on it. There are three ways to redefine the spectral density to overcome these difficulties. First, the spectral density is defined using the Fourier transformation of the relevant function; second, the finite-time Fourier transformation of the random process is used to define the spectral density; the third is to define the spectral density using the spectral decomposition of the steady random process. The three definition methods correspond to different uses. First, the premise of the first method is that a stable random process does not contain periodic components and the mean value is zero. In this way, the time difference of the related functions tends to decrease at infinity, therefore, the related functions alone cannot solve many problems and the requirements are too strict. For the second method, although a stable random process cannot undergo Fourier transformation for an infinite time, but for a finite interval, fourier transformation always exists. We can first describe the transformation on a finite time interval and take the limit on the time interval. This definition method is the basis for estimating the spectral density of the current fast Fourier Transformation (FFT; the third method is to generalized according to the theory of the generalized homophonic Analysis of Vina.
Harmonic Analysis, ACTA math, 55 (1930), 117-258, reconstructed the zero-mean Continuous Random Process in Mean Square using Fourier-stogis points, it is established by orthogonal. In addition, there are three spectral density establishment methods for non-Stable Random Processes. Due to word limit, the unit of spectral density is the square/frequency of G. That is, the ratio of the root-mean-square value of the function amplitude to the frequency. It is an important parameter for random vibration analysis.What is the international unit of power spectral density?For acceleration power spectral density, the unit of acceleration is m/s ^ 2, then the unit of acceleration power spectral density is (m/s ^ 2) ^ 2/Hz, the unit of Hz is 1/s, and the unit of the converted acceleration power spectrum density is m ^ 2/s ^ 3. similarly, for the displacement power spectral density, the unit is m ^ 2 * s. For the bending moment power spectral density, the unit is (N * m) ^ 2 * s displacement power spectrum -- m ^ 2 * s Velocity power spectrum -- m ^ 2/s acceleration power spectrum -- m ^ 2/s ^ 3Full-cycle samplingTo ensure full-cycle sampling, the sampling frequency fs and the number of sampling points n should be used together. In fact, the sampling data is exactly the whole cycle or multiple of the signal, that is, if the signal cycle is t, ensure that N/fs = L * t, where L is an integer. in actual sampling, full-cycle sampling is usually not possible. Even if you know the signal cycle and adopt synchronous sampling, some frequencies (Power Frequency and frequency doubling) in the signal can only be close to the full-cycle sampling, instead, all the frequency components (such as noise) in the signal cannot be fully sampled. the direct consequence of non-cyclic sampling is spectrum leakage, which makes the obtained frequency component inaccurate. Therefore, the sampling spectrum correction algorithm must be used for correction. the second consequence is that interference may occur for multiple frequency component signals with closer frequencies. this can only be achieved by adding a window to reduce the sides and refine the distance to eliminate such interference as much as possible.