CN106919732B - Method and apparatus for signal processing - Google Patents
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Abstract
The disclosure relates to a method and a device for signal processing, and belongs to the technical field of signal processing. A method for signal processing, comprising: acquiring an autocorrelation function of a signal; acquiring a double autocorrelation function of the signal according to the autocorrelation function; and carrying out Fourier transform on the double autocorrelation function to obtain a double autocorrelation frequency spectrum of the signal. The invention can realize the noise reduction processing of the signal containing the noise.
Description
Technical Field
The present disclosure relates to the field of signal processing technologies, and in particular, to a method and an apparatus for signal processing.
Background
The cutting force is a stable and reliable source of information during machining, and its magnitude and dynamic changes reflect the condition of the tool-workpiece interaction and the workpiece surface formation process during the cutting process. A large number of research results show that each tiny change of the cutting state can be reflected by the change of the cutting force, and the detection of the cutting force is one of the most widely studied and applied methods for monitoring the machining process at home and abroad at present. The method can be used for researching the related scientific problems of the cutting process, such as cutting mechanism research, process parameter analysis, material cutting performance research and the like, by monitoring the real-time change of the cutting force in the machining process and carrying out time sequence analysis or related data signal processing; technological parameters in the processing process are optimized, and the processing quality is improved; carrying out novel cutter design, cutter coating development and cutter cutting performance evaluation; and carrying out real-time monitoring on the cutting process, evaluating and early warning on tool abrasion and damage and realizing self-adaptive machining.
Frequency domain analysis is a method of transforming a time domain signal into the frequency domain for analysis. The method aims to decompose a complex time history waveform into single harmonic components through Fourier transform to study so as to obtain a frequency result of a signal and information of each harmonic and phase. Frequency domain analysis has extremely important application in the fields of radio communication, sonar systems, geophysical systems, image analysis, ultra-precision machining and the like.
The existing mainstream spectrum analysis method is as follows: a power spectral density calculated based on second order statistics. Although the power spectral density calculation is simple, the noise reduction capability for the signal is weak. In the ultra-precision machining process, the cutting force signal is influenced by complex environmental factors and contains more noise, and the power spectral density signal-to-noise ratio calculated by the traditional method is low, so that the information of tool nose vibration is not obtained by analyzing the cutting force frequency spectrum.
Therefore, a new method and apparatus for signal processing is needed.
The above information disclosed in this background section is only for enhancement of understanding of the background of the disclosure and therefore it may contain information that does not constitute prior art that is already known to a person of ordinary skill in the art.
Disclosure of Invention
The present disclosure provides a method and an apparatus for signal processing, which can implement noise reduction processing on a signal including noise.
Additional features and advantages of the disclosure will be set forth in the detailed description which follows, or in part will be obvious from the description, or may be learned by practice of the disclosure.
According to an aspect of the present disclosure, there is provided a method for signal processing, comprising:
acquiring an autocorrelation function of a signal;
acquiring a double autocorrelation function of the signal according to the autocorrelation function;
and carrying out Fourier transform on the double autocorrelation function to obtain a double autocorrelation frequency spectrum of the signal.
In an exemplary embodiment of the present disclosure, the signal is a cutting force signal s (t) for ultra-precision machining.
In an exemplary embodiment of the present disclosure, the cutting force signal is:
s(t)＝sin(ω1t+p1)+sin(ω2t+p2)+N(0,6)
wherein, ω is1＝2π*13000rad/s，p1＝20rad，ω2＝2π*14000rad/s，p2N (0,6) is white gaussian noise with mean 0 and variance 6 at 30 rad.
In an exemplary embodiment of the present disclosure, further comprising: and sampling the signal by adopting a preset sampling frequency.
In an exemplary embodiment of the present disclosure, further comprising: windowing the signal before obtaining an autocorrelation function of the signal.
According to an aspect of the present disclosure, there is provided an apparatus for signal processing, including:
the autocorrelation function acquisition module is used for acquiring an autocorrelation function of the signal;
a double autocorrelation function obtaining module, configured to obtain a double autocorrelation function of the signal according to the autocorrelation function;
and the double-autocorrelation spectrum acquisition module is used for carrying out Fourier transform on the double-autocorrelation function to acquire the double-autocorrelation spectrum of the signal.
In an exemplary embodiment of the present disclosure, the signal is a cutting force signal s (t) for ultra-precision machining.
In an exemplary embodiment of the present disclosure, the cutting force signal is:
s(t)＝sin(ω1t+p1)+sin(ω2t+p2)+N(0,6)
wherein, ω is1＝2π*13000rad/s，p1＝20rad，ω2＝2π*14000rad/s，p2N (0,6) is white gaussian noise with mean 0 and variance 6 at 30 rad.
In an exemplary embodiment of the present disclosure, further comprising: and the sampling module is used for sampling the signal by adopting a preset sampling frequency.
In an exemplary embodiment of the present disclosure, further comprising: a windowing module for windowing the signal before obtaining an autocorrelation function of the signal.
According to the method and the device for signal processing disclosed by the invention, the signal processing is carried out on the autocorrelation function to obtain the double autocorrelation function, and then the Fourier transform is carried out, so that the noise reduction processing can be carried out on the signal containing the noise.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention.
Fig. 1 schematically illustrates a flow chart of a method for signal processing according to an example embodiment of the present disclosure;
fig. 2 schematically shows a signal s (t) schematic according to an example embodiment of the present disclosure;
fig. 3 schematically illustrates an autocorrelation function r (h) according to an example embodiment of the present disclosure;
FIG. 4 schematically shows a power spectral density PSD diagram of a signal according to the prior art;
fig. 5 schematically shows a dual autocorrelation spectrum DCS schematic according to an example embodiment of the present disclosure;
fig. 6 schematically illustrates a block diagram of an apparatus for signal processing according to an example embodiment of the present disclosure.
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The drawings are merely schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus their repetitive description will be omitted.
Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of embodiments of the disclosure. One skilled in the relevant art will recognize, however, that the subject matter of the present disclosure can be practiced without one or more of the specific details, or with other methods, components, devices, steps, and the like. In other instances, well-known structures, methods, devices, implementations, materials, or operations are not shown or described in detail to avoid obscuring aspects of the disclosure.
The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the invention, as detailed in the appended claims.
Fig. 1 schematically illustrates a flow chart of a method for signal processing according to an example embodiment of the present disclosure.
As shown in fig. 1, in step S110, an autocorrelation function of the signal is acquired.
In an exemplary embodiment, the signal is a cutting force signal s (t) for ultra-precision machining. Of course, the disclosure is not limited thereto, and the invention can also be applied to processing other types of signal processing, such as sound signals, current signals, and the like.
The ultra-precision machining in the embodiment of the invention is a machining technology that the dimensional accuracy of a machined part is 0.1-0.01 micrometer, and the machining surface roughness reaches the order of Ra0.03-0.0051 micrometer. With the development of machining technology, the technical indexes of ultra-precision machining are changing continuously.
The ultra-precision cutting is mainly performed by a high-precision machine tool and a single-crystal diamond tool. Commonly referred to as Diamond Point Diamond Turning (SPDT).
In the embodiments of the present invention, the cutting force is a cutting force which is generated in the cutting process and acts on the workpiece and the tool in the same magnitude and in opposite directions. Popular saying: during cutting, the workpiece material resists the resistance generated by the cutting tool.
In step S120, a dual autocorrelation function of the signal is obtained according to the autocorrelation function.
In an exemplary embodiment, further comprising: and sampling the signal by adopting a preset sampling frequency.
In an exemplary embodiment, further comprising: windowing the signal before obtaining an autocorrelation function of the signal. The window function is a real function whose values are 0 except in a given interval, and aims to reduce the frequency spectrum leakage. Window functions that may be employed include triangular windows, hanning windows, scatter windows, gaussian windows, and the like, although the disclosure is not so limited.
The corresponding window function may be selected according to the composition of the signal and the purpose for which the signal is analyzed. For example, if the test signal has multiple frequency components and the purpose of the test is to focus on frequency points rather than energy magnitudes, a hanning window is typically selected; a flattop window may be used if the purpose of analyzing the signal is to look at the energy value at a certain periodic signal frequency point. Where the length of the window function is typically applied to be the same as the signal length.
It should be noted that, in general, the window function is symmetrical, and therefore, for the window function with the length N, the coefficients of the window function with the first half length of the window function may be stored, or the coefficients of the window function with the second half length of the window function may be stored, so that the storage space may be saved.
In step S130, fourier transform is performed on the double autocorrelation function to obtain a double autocorrelation spectrum of the signal.
The method for signal processing provided by the embodiment adopts a double autocorrelation spectrum based on a double autocorrelation function for signal analysis, and has the characteristics of small calculation amount and strong noise reduction capability.
The following is an example of the embodiment shown in fig. 2-5.
Fig. 2 schematically shows a signal s (t) schematic according to an example embodiment of the present disclosure.
The signal is exemplified as a cutting force signal s (t) for ultra-precision machining.
In ultra-precision machining, the cutting force signal s (t) contains dc, low frequency, high frequency and noise components. In the embodiment shown in fig. 2, the tip vibration frequency during the cutting process is about 14000 Hz. The spectral analysis method of the present disclosure is mainly used for studying the high-frequency vibration of the blade edge, and the following calculation of the double autocorrelation spectrum is described by taking the blade edge vibration frequency as about 14000Hz as an example. The cutting edge vibration frequency is related to the structural size of the tool and the cutting conditions, and therefore, the numerical value thereof may vary depending on the actual application.
Assuming that the cutting force signal s (t) is:
s(t)＝sin(ω1t+p1)+sin(ω2t+p2)+N(0,6)
wherein, ω is1＝2π*13000rad/s，p1＝20rad，ω2＝2π*14000rad/s，p2N (0,6) is White gaussian noise (White noise) with mean 0 and variance 6. Wherein, ω is2The corresponding frequency 14000Hz is the vibration frequency of the knife edge. Omega1The corresponding frequency of 13000Hz is the frequency of the blade edge due to damping effect when it vibrates.
White noise, or white noise, is a random signal or random process with a constant power spectral density. The power spectral density is constant, that is, the energy of the signal is the same at each frequency. Since white light is a mixture of colors of different frequencies, noise having a desired energy at the same frequency is called "white".
Discrete signal samples obtained by sampling the cutting force signal s (t). Wherein the sampling frequency can be more than twice of the vibration frequency of the tool nose. In the following examples, 50,000Hz was used as the sampling frequency.
s (t) is a continuous signal containing white noise, and N sample points sn are obtained through sampling (the sampling frequency is fs), namely s 0, s1, s 2, …, s N-1, and when N is not equal to 0,1,2 … N-1, s N takes a value of 0. The autocorrelation function R (h) of s [ n ] is then:
wherein the content of the first and second substances,
sample mean for s:
assuming that the sampling time is 0.1s and the sampling frequency is 50000Hz, the autocorrelation function R (h) of the measured cutting force signal s (t) is shown in FIG. 3.
In the prior art, the above autocorrelation function r (h) is directly used to obtain the power spectral density PSD (PSD) of the signal, as shown in fig. 4.
In physics, a signal is typically represented in the form of a wave, such as an electromagnetic wave, random vibration, or acoustic wave. The power carried by a wave per unit frequency is obtained when the spectral density of the power of the wave is multiplied by a suitable coefficient, which is called the power spectral density of the signal. The unit of power spectral density is typically expressed in watts per hertz (W/Hz), which is expressed using wavelength rather than frequency, i.e., watts per nanometer (W/nm).
In this embodiment, the dual autocorrelation function rr (h) corresponding to the signal s [ n ] is continuously calculated:
wherein
Mean of the autocorrelation function r (h).
Then, a double autocorrelation spectrum dcs (double Correlation spectrum) of the signal is obtained according to the following formula according to the above double autocorrelation function rr (h):
where k is 0,1, 2.., N-1, i is an imaginary unit, x (k) is a fourier series, and f is a frequency:
fig. 5 schematically shows a dual autocorrelation spectrum DCS schematic according to an example embodiment of the present disclosure.
As can be seen from a comparison of the two graphs of fig. 4 and 5, the dual autocorrelation spectrum DCS has a significantly reduced background noise and an improved signal-to-noise ratio compared to the conventional power spectral density PSD.
In the embodiments of fig. 3 to 5, the original signal s (t) is discretized to obtain the double autocorrelation spectrum DCS, but in other embodiments, the continuous original signal s (t) may be directly subjected to signal processing to obtain the double autocorrelation spectrum DCS.
The autocorrelation function R (t) of the successive signals s (t) is determined:
in the formula (4), t is time, s (t) is cutting force measured by the sensor at the time t, and tau is delay time.
In the prior art, the fourier transform is directly performed on the autocorrelation function to obtain the power spectral density PSD:
in the embodiment of the present invention, the dual autocorrelation function rr (t) corresponding to the signal s (t) is continuously calculated:
then, a double autocorrelation spectrum dcs (f) corresponding to the signal s (t) is calculated according to the double autocorrelation function rr (t):
if the original signal s (t) is a periodic function, its autocorrelation function R (t) is also a periodic function, and the periods of the original signal s (t) and its autocorrelation function R (t) are the same. The Fourier transform is carried out by replacing the autocorrelation function R (t) with the double autocorrelation function RR (t) of the original signal s (t), so that the amplitude of periodic components in the signal is increased, and the amplitude of non-periodic components in the signal is reduced. And compared with a high-order spectrum, the double autocorrelation spectrum is only a second-order spectrum, and the calculation amount is small. Therefore, the spectrum based on the double autocorrelation function rr (t) in the present embodiment has the characteristics of small calculation amount and strong noise reduction capability.
Fig. 6 schematically illustrates a block diagram of an apparatus for signal processing according to an example embodiment of the present disclosure.
As shown in fig. 6, the apparatus 200 for signal processing includes an autocorrelation function obtaining module 210, a double autocorrelation function obtaining module 220, and a double autocorrelation spectrum obtaining module 230.
Wherein the autocorrelation function acquiring module 210 is configured to acquire an autocorrelation function of the signal.
Wherein the dual autocorrelation function obtaining module 220 is configured to obtain a dual autocorrelation function of the signal according to the autocorrelation function.
The double autocorrelation spectrum obtaining module 230 is configured to perform fourier transform on the double autocorrelation function to obtain a double autocorrelation spectrum of the signal.
In an exemplary embodiment, the signal is a cutting force signal s (t) for ultra-precision machining.
In an exemplary embodiment, the cutting force signal is:
s(t)＝sin(ω1t+p1)+sin(ω2t+p2)+N(0,6)
wherein, ω is1＝2π*13000rad/s，p1＝20rad，ω2＝2π*14000rad/s，p2N (0,6) is white gaussian noise with mean 0 and variance 6 at 30 rad.
In an exemplary embodiment, further comprising: and the sampling module is used for sampling the signal by adopting a preset sampling frequency.
In an exemplary embodiment, further comprising: a windowing module for windowing the signal before obtaining an autocorrelation function of the signal.
For other contents in the embodiments of the present invention, reference is made to the contents in the above embodiments of the present invention, and further description is omitted here.
The disclosed method and apparatus for signal processing performs fourier transform by replacing the autocorrelation function r (t) with the double autocorrelation function rr (t) of the original signal s (t), so that the calculated spectrum is a double autocorrelation spectrum. The double autocorrelation spectrum has higher signal-to-noise ratio compared with power spectral density, which has positive significance for signal harmonic analysis. The method can be used for frequency domain analysis of the ultra-precision machining cutting force based on the double autocorrelation function, and compared with a traditional power spectral density calculation method, the double autocorrelation spectrum calculation algorithm improves the noise reduction capability of signals and improves the signal-to-noise ratio.
Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.
Exemplary embodiments of the present disclosure are specifically illustrated and described above. It is to be understood that the present disclosure is not limited to the precise arrangements, instrumentalities, or instrumentalities described herein; on the contrary, the disclosure is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
Claims (4)
1. A method for signal processing, comprising:
the method comprises the following steps of sampling a cutting force signal s (t) by adopting a sampling frequency of 50000Hz to obtain N discrete signals s [ h ], wherein h is 0,1, … and N-1, wherein the cutting force signal s (t) comprises direct current, low frequency, high frequency and noise components, and N is a positive integer;
obtaining an autocorrelation function of the discrete signal s [ h ];
obtaining a double autocorrelation function of the discrete signal s [ h ] according to the autocorrelation function;
fourier transform is carried out on the double autocorrelation function, and a double autocorrelation frequency spectrum of the discrete signal s [ h ] is obtained;
the cutting force signal s (t) is:
s(t)＝sin(ω1t+p1)+sin(ω2t+p2)+N(0,6)
wherein, ω is1＝2π*13000rad/s，p1＝20rad，ω2＝2π*14000rad/s，p230rad, N (0,6) is gaussian white noise with mean 0 and variance 6;
the autocorrelation function R (h) of the discrete signal s [ h ] is:
wherein the content of the first and second substances,
sample mean for s:
when h ≠ 0,1,2 … N-1, s [ h]The value is 0;
the double autocorrelation function of the discrete signal s [ h ] is:
wherein the content of the first and second substances,
is the mean of the autocorrelation function r (h).
2. The method of claim 1, further comprising: windowing the signal before obtaining an autocorrelation function of the signal.
3. An apparatus for signal processing, comprising:
a sampling module, configured to sample a cutting force signal s (t) with a sampling frequency of 50000Hz to obtain N discrete signals s [ h ], h is 0,1, …, N-1, where the cutting force signal s (t) includes dc, low frequency, high frequency, and noise components, N is a positive integer
An autocorrelation function obtaining module, configured to obtain an autocorrelation function of the discrete signal s [ h ], where an autocorrelation function r (h) of the discrete signal s [ h ] is:
wherein the content of the first and second substances,
sample mean for s:
when h ≠ 0,1,2 … N-1, s [ h]The value is 0;
a double autocorrelation function obtaining module, configured to obtain a double autocorrelation function of the discrete signal s [ h ] according to the autocorrelation function, where the double autocorrelation function of the discrete signal s [ h ] is:
wherein the content of the first and second substances,
is the mean of the autocorrelation function r (h);
the double-autocorrelation spectrum acquisition module is used for carrying out Fourier transform on the double-autocorrelation function to acquire a double-autocorrelation spectrum of the signal;
the cutting force signal s (t) is:
s(t)＝sin(ω1t+p1)+sin(ω2t+p2)+N(0,6)
wherein, ω is1＝2π*13000rad/s，p1＝20rad，ω2＝2π*14000rad/s，p2N (0,6) is white gaussian noise with mean 0 and variance 6 at 30 rad.
4. The apparatus of claim 3, further comprising: a windowing module for windowing the signal before obtaining an autocorrelation function of the signal.
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