summary
Leveraging the advantages of virtual instruments, a data acquisition and analysis system was designed using the high-performance PCI9846 data acquisition card manufactured by ADLINK Technology, which has 4 channels, 16-bit sampling accuracy, and a maximum sampling rate of 40MS/s, and National Instruments (NI) LabVIEW 8.6. Discrete spectrum correction methods such as ratio correction, energy centroid correction, FFT+FT continuous refinement analysis, and phase difference method were employed to perform spectrum correction analysis on the signal, thereby improving the accuracy of signal analysis.
A complete signal analysis system usually consists of three parts: signal acquisition and collection, signal analysis and processing, and result output and display. Traditional test instruments are basically in the form of hardware or fixed software, and the instruments are defined and manufactured by the manufacturers. The design of traditional instruments is more complex and less flexible. They have not broken away from the mode of independent use and manual operation. The entire test process is almost limited to simply imitating the steps of manual testing, which is not suitable for some more complex occasions with more test parameters[1]. Compared with traditional instruments, virtual instruments have obvious advantages such as high efficiency, openness, ease of use and flexibility, powerful functions, high cost performance and good operability. Specifically, they are characterized by high intelligence, strong processing power, strong reusability, low system cost and strong operability[2]. Based on the advantages of virtual instruments, a data acquisition and analysis system was designed using PCI9846 and LabVIEW for automotive NVH analysis.
1 System Composition
Virtual instruments are becoming a popular instrument configuration solution worldwide. Based on computers and combined with appropriate hardware and software, virtual instruments complete data acquisition and processing. Their structure is open; they combine a computer platform with hardware modules featuring standard interfaces and development testing software to form an instrument system. This system is versatile, flexible, and facilitates the development of testing applications.
1.1 Hardware Configuration
The hardware system is based on a computer, with the data acquisition card inserted into it as the main functional component. The measured signal is received by the data acquisition card and then transmitted into the computer, where it is analyzed and processed by the corresponding software. Therefore, the data acquisition card is the key to the successful design of the virtual instrument [3].
The data acquisition card used in this system is the PCI9846 produced by ADLINK Technology. The PCI9846 is a high-speed digitizer with 4 channels, a sampling accuracy of 16 bits, and a sampling frequency of 40MS/s. It provides high precision, low noise and high dynamic range performance, high density and high accuracy, and is designed for high-frequency and high dynamic range signals with input signal frequencies up to 20MHz. The analog input range can be programmed to ±1V/±0.2V or ±5V/±0.4V. Equipped with onboard memory of up to 512MB, the PCI9846 is freed from the constraints of the PCI bus, enabling it to store waveforms for longer periods of time [4].
1.2 Software Platform
The software part is the heart of the virtual instrument. At present, the most widely used graphical programming software development platform based on virtual instruments is LabVIEW (Laboratory Virtual Instrument Engineering Workbench) developed by National Instruments (NI). LabVIEW is a graphical programming development environment based on G (Graphic) language. It is widely accepted by industry, academia and research laboratories as a standard language for developing data acquisition systems, instrument control software and analysis software. When programming with this language, you basically do not write program code. It is an ideal language for scientific research and engineering applications. It makes full use of the terms, icons and concepts familiar to technicians, scientists and engineers. Therefore, LabVIEW is a tool for end users. LabVIEW integrates all the functions of communicating with hardware and data acquisition cards that meet the GPIB, VXI, RS-232 and RS-485 protocols. It also has built-in library functions that facilitate the application of software standards such as TCP/IP and ActiveX [5]. It is a powerful and flexible software. It can be used to easily build your own virtual instruments. Its graphical interface makes the programming and use process vivid and interesting. It can enhance users' ability to build scientific and engineering systems, providing a convenient way to implement instrument programming and data acquisition systems. Using it for principle research, design, testing, and instrument system implementation can greatly improve work efficiency.
LabVIEW offers a rich library of functions, significantly shortening development cycles, and the applications developed using it are easy to maintain and expand. Developing data acquisition and analysis applications using the LabVIEW development environment, by combining the PCI9846 data acquisition card with the flexible and convenient LabVIEW application development platform, can reduce development costs, shorten development cycles, and make development convenient and efficient.
1.3 LabVIEW Control and Acquisition Card
PCI9846 provides a LabVIEW driver. When installing the driver, it will automatically search for the LabVIEW directory and then copy the necessary files to the corresponding folder. If LabVIEW is not installed on the system or its version is lower than 6.0, the driver installer will pop up a dialog box to prompt you to update the LabVIEW version. After the LabVIEW driver is installed, you can use PCI9846 in LabVIEW to perform data acquisition [4].
After the LabVIEW driver is installed, a corresponding item as shown in Figure 1 will be added to the function palette. In this article, we will directly use "DAQPilotExpressVI". After completing the corresponding settings according to the prompts, data acquisition can be achieved (Figure 2).
Figure 1. New items in the LabVIEW Functions palette
Figure 2 Configuration Wizard
2. Signal Analysis
After data acquisition, it is essential to analyze the data to extract relevant information. The data analysis in this system primarily focuses on the frequency domain. Signal analysis and processing is a crucial component of LabVIEW, providing a large number of highly specialized signal analysis and processing functions. For common signal analyses, LabVIEW's built-in functions are sufficient; however, for more complex signal processing, custom functions must be written.
The frequency, amplitude and phase of the discrete Fourier transform and spectrum analysis of harmonic signals may have large errors. Theoretically, when a rectangular window is added to a single-frequency harmonic signal, the maximum amplitude error of the discrete spectrum analysis can reach 36.4%. Even when other windows are added, this error cannot be completely eliminated. When the Hanning window is added and only amplitude recovery is performed, the maximum amplitude error is still as high as 15.3%. Regardless of the window function added, the maximum phase error of the discrete spectrum analysis is as high as ±90 degrees, and the maximum frequency error is ±0.5 frequency resolutions. Therefore, the results of spectrum analysis can only be qualitatively analyzed and solved in many fields, which greatly limits the engineering application of this technology, especially in mechanical vibration and fault diagnosis. Therefore, it is necessary to correct the parameters of each frequency component obtained by discrete spectrum analysis in order to obtain more accurate frequency, amplitude and phase estimates. Therefore, it is necessary to study the correction theory and technology of discrete spectrum to eliminate or greatly reduce this error and improve the analysis accuracy. For discrete spectrum of single frequency component or multi-frequency component with large intervals, correction is performed[6].
Currently, there are four methods for correcting amplitude or power spectra at home and abroad [6]: ratio correction method (interpolation method), energy centroid correction method, FFT+FT continuous refinement analysis Fourier transform method, and phase difference method; the phase difference method is further divided into time shift method, window length change method, and comprehensive method. Theoretically, when the signal is free of noise, the ratio method and the phase difference method are accurate correction methods, while the energy centroid method and FFT+FT spectrum continuous refinement analysis Fourier transform method are highly accurate approximation methods.
With the development and continuous improvement of discrete spectrum correction technology, it is increasingly being applied to analyze various practical problems and dynamic signal analysis systems. Discrete spectrum correction theory has been, or will be, widely applied in the following fields:
(1) Various dynamic signal analyzers and computer-aided testing systems;
(2) Vibration signal of rotating machinery. Rotating machinery with sliding bearings usually has a very stable operating speed and requires phase as an analysis parameter. In this case, the ratio correction method is the best choice.
(3) Engine and other torsional vibration signals. For steady-state torsional vibration signals, it is only necessary to accurately calculate the amplitude of each harmonic. Since the three-point convolution correction method is not affected by small fluctuations in rotational speed, it is the best choice for steady-state torsional vibration signals.
(4) Applications in the field of instrumentation: It has been applied to instruments such as vortex flowmeters and electrical parameters of power systems that require precise frequency measurement to calculate physical quantities.
(5) Power system harmonic analysis;
(6) Improve accuracy in laser Doppler velocimetry;
(7) High-precision frequency and amplitude calibration system. At present, there is still a gap in China in terms of instruments for accurately calibrating the frequency and amplitude of dynamic signals. Calibration instruments can be developed by using the ratio correction method in conjunction with a high-precision A/D board to fill this gap.
(8) Precisely analyze the spectrum of various vibration signals;
(9) Cyclic stationary demodulation analysis uses discrete spectrum to correct the modulation frequency and amplitude after demodulation, which greatly improves the analysis accuracy and can extract fault information more accurately.
(10) Military applications of radar precision ranging and electronic countermeasures.
2.1 Ratio Correction Method (Interpolation Method)
This method utilizes the ratio of the window spectral functions of two spectral lines near the peak of the main lobe, where the difference is 1 after frequency normalization, to establish an equation with the normalized correction frequency as the variable. The normalized correction frequency is then solved, and frequency, amplitude, and phase corrections are performed. This method is applicable to discrete spectrum correction when the theoretical expression of the Fourier transform of the applied symmetric window function is known.
The correction frequency is:
Characteristics of the ratio correction method:
(1) A general discrete spectrum correction method applicable to known normalized window function spectrum analytical expressions; it can accurately correct the frequency, amplitude and phase of the discrete spectrum of a single-frequency harmonic signal, greatly improving the accuracy of discrete spectrum analysis;
(2) The problem of accurately solving the parameters (frequency, amplitude and phase) of multiple frequency components with large intervals (more than 5 frequency resolutions) has been systematically solved in theory and practice;
(3) The algorithm is simple and the calculation speed is fast;
(4) Without considering the influence of noise in the signal, the ratio method is an accurate correction method. After correction, the frequency, amplitude and phase are the theoretical values, but they will be affected by digital truncation error in digital calculation and produce a very small error.
(5) Not applicable to the correction of signals with excessively dense frequency components and discrete spectrum analysis of continuous frequency component signals.
2.2 Energy Center of Gravity Correction Method
This method is a discrete spectrum correction method derived from the characteristic that the energy centroid of the discrete spectrum of a symmetric window function infinitely approaches or is near the origin. It is a general discrete spectrum correction method applicable to various symmetric windows. Taking the Hanning window as an example, since the power spectral values of its side lobes are very small, based on the characteristic of its energy centroid, if X is set to the range of [-0.5, 0.5], the center coordinates of the main lobe can be accurately obtained using the spectral lines with larger power spectral values within the main lobe. Let the sampling frequency be , the number of spectral points be N, the spectral line number of the peak value within the main lobe be m, Yi be the value of the i-th spectral line of the power spectrum, and x0 be the center of the main lobe. The frequency correction formula is:
The corrected phase can be obtained by combining equations (3) and (4).
Characteristics of the energy center of gravity correction method:
(1) A general discrete spectrum correction method applicable to any spectrum with a symmetric window function, which can greatly improve the analysis accuracy of discrete spectrum;
(2) Compared with other correction methods, it can directly correct multiple average power spectra;
(3) The algorithm is simple and the calculation speed is fast;
(4) The error caused by the interference phenomenon of negative frequency components and closely spaced multi-frequency components has little impact on accuracy;
(5) The correction accuracy is related to the window function; the correction accuracy is higher when the Hanning window is added.
(6) The correction accuracy is related to the number of points involved in the correction. The more points there are, the higher the correction accuracy for a single frequency component, but the greater the frequency interval between two adjacent spectral peaks is required.
(7) Without considering the influence of noise in the signal, the energy centroid method is a highly accurate approximate correction method. The frequency, amplitude and phase after correction are not the theoretical values, but the error is very small.
(8) Not applicable to the correction of signals with excessively dense frequency components and discrete spectrum analysis of continuous frequency component signals.
2.3 FFT+FT Continuous Refinement Analysis Fourier Transform Method
This method essentially uses FFT to generate a panoramic spectrum, and then applies an improved continuous Fourier transform (FT) to the local area to be refined, resulting in a spectrum with extremely high local refinement accuracy. After performing FFT on the sampled signal, L-point equally spaced spectral analysis is performed within a specified frequency range.
Characteristics of the FFT+FT continuous refinement analysis Fourier transform method:
(1) A general discrete spectrum correction method applicable to any spectrum with a symmetric window function, which can greatly improve the analysis accuracy of discrete spectrum; it can greatly improve the frequency resolution and the calculation accuracy of amplitude and phase without increasing the sampling length;
(2) The calculation speed is much slower than other methods, making it unsuitable for real-time spectrum analysis and correction;
(3) Unlike the complex modulation refinement band selection spectrum analysis method, since the length of the window is not increased, it can only refine the amplitude and phase of the local frequency of the signal. It cannot separate the already very dense multi-frequency signal with main lobe overlap and interference into multiple single-frequency component signals without main lobe overlap and interference. Therefore, it is not suitable for the correction of signals with too dense frequency components and discrete spectrum analysis of continuous frequency component signals.
2.4 Phase Difference Method
Phase difference methods are categorized into time-shifting, window-length-changing, and combined methods. Essentially, they involve continuously sampling the same signal to obtain two time series, where the second time series lags the first by a certain number of points. The same or different window functions are applied to these two time series, and two FFT (or DFT) analyses with different or the same number of points are performed. The phase difference between the corresponding peak spectral lines is then used for discrete spectrum correction. This method is suitable for discrete spectrum correction under various symmetrical window conditions. There are three main phase difference correction methods: the first is the window-length-changing method; the second is the time-domain shifting method; and the third is the combined correction method, which combines time-domain shifting, window-length changing, and the application of different window functions. This combined method is suitable for discrete spectrum correction under various symmetrical window conditions.
This method uses the phase difference after FFT of two time series for spectral correction. The original single-frequency component signal is sampled in two consecutive segments, and then Fourier transforms are performed on these two segments. The phase difference of the corresponding discrete spectral lines is used to correct the accurate frequency and phase at the spectral peak. Both signals are subjected to the same window function before Discrete Fourier Transform. The transformed phase-frequency functions not only have a linear relationship within the main lobe of the window function but also have the same slope. Therefore:
Characteristics of phase difference correction method:
(1) It has good versatility. Its correction method is not affected by the different window functions applied. It is a general discrete spectrum correction method that is applicable to any symmetric window function.
(2) The algorithm is simple and the calculation speed is fast;
(3) It has a strong ability to resist noise interference;
(4) Without considering the influence of noise in the signal, the phase difference method is an accurate correction method. After correction, the frequency, amplitude and phase are the theoretical values, but they will be affected by digital truncation error in digital calculation and produce a very small error.
(5) Not applicable to the correction of signals with excessively dense frequency components and discrete spectrum analysis of continuous frequency component signals.
In this system, in order to improve the accuracy of data analysis, based on the principles of four commonly used spectrum correction methods—ratio correction method, energy centroid correction method, FFT+FT continuous refinement analysis Fourier transform method, and phase difference method—corresponding functions were written in LabVIEW 8.6 to perform spectrum correction processing on the data.
3. Summary
Using ADLINK's high-performance data acquisition card PCI9846 and LabVIEW, combined with four latest spectrum correction methods, a data acquisition and analysis system was designed for automotive vibration data analysis.
