CN110233626B - Mechanical vibration signal edge data lossless compression method based on two-dimensional adaptive quantization - Google Patents
Mechanical vibration signal edge data lossless compression method based on two-dimensional adaptive quantization Download PDFInfo
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Abstract
The invention relates to a mechanical vibration signal edge data lossless compression method based on two-dimensional adaptive quantization, which comprises data segmentation, block data transformation, adaptive quantization and data coding. 1) Dividing original time domain data into blocks with fixed width, converting the original one-dimensional data into two-dimensional data, and performing two-dimensional orthogonal transformation; 2) Quantizing the two-dimensional data after orthogonal transformation in a frequency domain; 3) Inversely quantizing the quantized data, and solving the quantization error between the inversely quantized data and the original data matrix; 4) And coding the quantized data matrix, the quantized error data, the orthogonal transformation matrix and the positive and negative value information matrix, and coding the data by using a two-dimensional zero coding, bit coding and range coding method and putting the coded data into a data stream for transmission. After receiving the compressed data, the data center decodes the lossless coded data, then carries out inverse quantization and inverse orthogonal transformation, and can restore the original data without loss by adding error data.
Description
Technical Field
The invention belongs to the technical field of lossless data compression, and relates to a lossless compression method for mechanical vibration signal edge data based on two-dimensional adaptive quantization.
Background
Advanced condition monitoring and fault diagnosis techniques are important technical means for ensuring healthy and stable operation of mechanical equipment. The acquisition and analysis of mechanical vibration signals is a basic method for condition monitoring and preventive maintenance. When acquiring mechanical vibration signals, the acquisition system typically requires a higher sampling frequency of 5-20kHz in order to obtain as much condition information as possible. In long-term condition monitoring, large amounts of data will be generated in a short time, which presents a huge challenge to storage space and data transmission, especially in certain remote or wireless monitoring systems where data transmission and storage are limited. One possible solution is to employ data compression methods to compress the raw data collected, reducing the total amount of data transmitted or stored.
Data compression is a technical method for reducing the data volume to reduce the storage space and improve the transmission, storage and processing efficiency of the data without losing the original data information. Or reorganize the data according to a certain algorithm, and reduce the redundancy and storage space of the data. According to the decompression methods corresponding to different compression methods, the original data file can be basically or completely and accurately reconstructed from the compressed data file. Data compression methods can be classified into two broad categories, lossless compression (where the reconstructed data is identical to the original data) and lossy compression (where the reconstructed data is allowed to deviate from the original data, and thus a better compression effect than lossless compression can be generally achieved), depending on whether the original data file can be recovered without distortion by compressing the data file.
In recent years, some studies have been made on a data compression method of a mechanical vibration signal. Guo et al propose a data compression method based on EEMD for the need of remote wireless machine condition monitoring. Oltean et al first transform the original signal using a lapped orthogonal transform method and then perform data compression using subband coding. Alsalaet et al studied a mechanical vibration signal data compression method combining MDCT and EHCC. King et al proposed a two-stage compression method for rolling bearing fault monitoring applications. Lu et al have studied undersampling techniques suitable for mechanical vibration wireless sensor networks. All of these methods can significantly reduce the amount of raw data, but can result in some raw data being lost. However, less research has been conducted on methods for lossless compression of mechanical vibration signals.
Disclosure of Invention
In view of this, the present invention aims to solve the problem of loss of the edge data of the mechanical vibration signal in the compression process, and implement lossless compression of the data, and provides a lossless compression method capable of implementing the edge data of the mechanical vibration signal.
In order to achieve the purpose, the invention provides the following technical scheme:
a mechanical vibration signal edge data lossless compression method based on two-dimensional adaptive quantization comprises the following steps:
s1: the method comprises the following steps that an acquisition node located on the edge side of a network cuts acquired mechanical vibration signal data into blocks in a fixed length M through a sensor, and an original time domain two-dimensional data matrix X with the total number of blocks being L is obtained, wherein the total length of original data is L M:
s2: on an acquisition node at the edge side of the network, original time domain data is subjected to overlap orthogonal transformation (LOT) to convert the time domain data into frequency domain data, the subsequent processing process is facilitated by utilizing the characteristic of energy concentration of mechanical vibration signal data in the frequency domain, and the matrix form of the overlap orthogonal transformation is described as follows:
Y＝T'*X (1)
wherein Y is a frequency domain matrix, X is original two-dimensional time domain data, T is an orthogonal transformation matrix, T is a (L M) X (L M) order block diagonal matrix, and T' is a transpose matrix of T;
the conversion of the original data into the frequency domain means that if data is analyzed in the time domain of the mechanical vibration signal, the variation amplitude between adjacent data is relatively large and the variation rate is fast, making it difficult to compress the mechanical vibration signal data. After the orthogonal transformation method is used for processing, strong correlation exists in a frequency domain, and a strong energy accumulation characteristic is shown, so that an orthogonal transformation matrix W with the characteristic is selected. Further converting the raw data into the frequency domain.
Similar to the conventional orthogonal transformation, the overlapped orthogonal transformation divides the signal into L segments, but each segment has a length of M1, and M < M1<2M is satisfied, that is: there is signal overlap of length M1-M between two adjacent segments, the overlap orthogonal transformation still changes into coefficient vector with length M, so that the signal length in the changing domain is not changed, and the transformation matrix of LOT is set as:
wherein P is 0 For M1xM order matrix, since only one segment of signal overlaps at the beginning and end of the signal, P needs to be defined separately 1 And P 2 (ii) a To ensure T L Are orthogonal, requiring P 0 Must be orthogonal, i.e.:
P′ 0 P 0 ＝I
at the same time, the overlap function of two adjacent segments must also satisfy orthogonality, i.e.:
P′ 0 WP 0 ＝P 0 WP′ 0 ＝0
wherein the transfer matrix W is:
wherein, I is M1-M order unit matrix, M1=2M is selected, therefore, the process of solving the frequency domain matrix Y through orthogonal variation in the formula (1) is written as the following form:
s3: the frequency domain matrix Y obtained after the orthogonal transformation is represented as follows:
the invention adopts the overlapped orthogonal transformation because the overlapped orthogonal transformation has several characteristics which are superior to other changes, and the characteristics are as follows:
1) Entropy preservation: the Jacobin determinant with normalized orthogonal variation has a value of 1, which means that no information is lost by the orthogonal transformation itself, so that the information can be transmitted by using the transmission transformation coefficient
2) Energy conservation: the two-dimensional Passevel theorem is satisfied, and the signal energy in the transform domain is equal to that of the original space domain. Thus, when the signal energy in the space domain is completely converted into a certain transform domain, a limited number of space sampling values can be completely recovered by the weighting of a limited number of transform coefficients to the base vector.
3) Decorrelation: orthogonal variation enables components of the vector signals to be uncorrelated, and a covariance matrix of the transform domain signals is a diagonal; under certain conditions (e.g., increasing transform size) the coefficients can even be made independent of each other, thus making the memoryless source a memoryless source.
4) Energy redistribution and concentration: the most important feature of the orthogonal transformation is that the energy is mainly concentrated in the low frequency or low order region of the signal, making most of the transform coefficients zero or small. The bit with smaller energy can be discarded if the image quality allows, which is the root cause of the high data compression rate achieved by the orthogonal transformation.
5) If the orthogonal change exists, the inverse change exists and the change is unique; the orthogonal change is simplest in calculation, if the orthogonal change is a discrete signal, and N is a finite value, the change is only simple matrix and vector operation, and the inverse change does not need inversion, so that the characteristic provides a condition for realizing the error calculation of the inverse orthogonal change under the condition that the storage space of the wireless sensor network node is limited.
6) The replacement of DCT with LOT is mainly based on the following two considerations: (1) The LOT and the DCT are very similar in implementation process, and the LOT fast algorithm is completed on the basis of the DCT fast algorithm; (2) The greatest advantage of LOT over DCT is that it can effectively remove blocking artifacts, thereby facilitating maximum compression of the data.
S4: in order to facilitate data compression and processing, values in a two-dimensional matrix Y are converted into positive values, positive and negative value information corresponding to the values in the Y is stored by a P matrix, 1 in the P matrix is positive correspondingly, and-1 in the P matrix is negative correspondingly, and the converted positive two-dimensional frequency domain matrix is represented by B;
s5: the quantization degree is controlled by using a single-valued quantization bit number Q, L is the number of data segmentation blocks, M is the length of each block, Q represents the total number of the distributed quantization bit numbers, and the calculation mode of Q is as follows:
Q＝q*M*L (3)
s6: assigning a quantization bit for each value in the B matrix:
firstly, the positions of the first three corresponding maximum values in the positive two-dimensional frequency domain matrix B are found, and max _1, max \u2 and max \u3 are respectively used for representing the maximum value, the second largest value and the third largest value; dividing the value corresponding to the maximum value max _1 by 2 and comparing the divided value with max _2 and max _ 3; if max _1 is larger than max _2, modifying the value of the position (i, j) in B corresponding to max _ 1; if max _1 is smaller than max _2 and larger than max _3, modifying the value of the position (i, j) in B corresponding to max _1, and exchanging the values pointed by max _1 and max _2 to ensure that max _1 always points to the maximum value; if the value of max _1 is less than the value of max _3, after the corresponding value in the matrix B is modified, max _1 points to max _2, max _2points to max _3, and the third largest value is found in the matrix B and is pointed to the value by max _ 3; every time the operation corresponding to the (i, j) position in the matrix is carried out, Q minus 1 operation is carried out on the total allocation position, the value corresponding to the (i, j) position in the quantization digit matrix Z (L x M) is increased by 1, and then a quantized matrix B and a quantization digit matrix Z are obtained;
max_1＝max_1/2 (4)
Q＝Q-1 (5)
B (i,j) ＝B (i,j) /2 (6)
Z (i,j) ＝Z (i,j) +1 (7)
s7: step S6 is repeated until all quantization bits are allocated, i.e., the value of Q becomes 0, and Q quantization bits are allocated in total to the total number of coefficients, resulting in B (Q) and Z (Q).
S8: averaging the coefficient matrix B (Q) obtained after the last quantization, and storing the value as an average quantization step S;
s9: and calculating the maximum quantization value corresponding to each value in the original positive two-dimensional frequency domain matrix B according to the average quantization step S, wherein the calculation mode is as follows:
s10: calculating the maximum quantization bit value b corresponding to each value in the coefficient matrix max To obtain the maximum quantization bit matrix B max The calculation method is as follows:
s11: to achieve lossless compression, a matrix B of maximum quantization bits is used max PeaceAnd carrying out inverse quantization on the average quantization step S to obtain an inverse quantization matrix, wherein the calculation mode is as follows:
s12: and carrying out inverse orthogonal transformation on the inverse quantization matrix to obtain a restored original matrix, wherein the calculation mode is as follows:
where P is the positive-negative value information indicated in step S4;
s13: and solving errors with the original matrix, wherein the error matrix is represented by E, and the obtained error matrix is as follows:
s14: using two-dimensional zero coding method to carry out error matrix E and maximum quantization bit matrix B max Coding is carried out, when data 0 continuously appears, the coding mode enters a zero counting coding mode to store the number of zero appearance, when non-zero data is encountered, the coding mode exits the zero counting coding mode to directly store, and the coding mode is obtained through the steps
And
the compression efficiency is greatly improved;
s15: considering the particularity of the positive and negative value information matrix P, since the matrix only has 1 and-1 data, 0 is used to replace-1; the binary representation method of bit coding, namely 0 and 1, namely data with the size of 1bit is adopted; while using the two-dimensional zero mentioned in step S14The coding method counts the continuous 0 and 1 and stores the occurrence times thereof, and the coding method obtains the result through the step
And
s16: the transmission data is coded using a range coding method which first gives a sufficiently large range of integers and estimates of the probability of the occurrence of a symbol or number, the initial range being easily divided into sub-ranges whose size is proportional to the probability of the symbol they represent. Then, each symbol of the message is encoded in turn by reducing the current range to a sub-range that corresponds exactly to the next symbol to be encoded; will be provided with
After range coding, the data and S are put into a data stream as original data and are transmitted as compressed data;
s17: after receiving the data in the data stream, the data center firstly pairs
Decoding according to two-dimensional zero coding and bit coding to obtain error data E and maximum quantization bit B max An orthogonal transformation matrix T and a positive and negative value information matrix P; and then, restoring the data according to the processes of the step S11 and the step S12, summing the obtained matrix and the error matrix E to obtain original data, and realizing lossless compression and recovery of the data:
。
further, step S5 uses quantization coefficient Q to calculate when calculating the total number of Q quantization bits, Q is 0.856, so as to implement lossless compression of data.
Further, step S11 is to perform two-dimensional zero-coding and bit-codingFirstly, inverse orthogonal transformation and inverse quantization processes are carried out, and error calculation is carried out; error data E, orthogonal transformation matrix T, positive and negative value information matrix P and maximum quantization bit B max And zero counting and range coding can show better compression performance.
The invention has the beneficial effects that: the invention solves the data storage and transmission problems of a large amount of vibration signal data generated in the long-term state monitoring of mechanical equipment.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
Drawings
For a better understanding of the objects, aspects and advantages of the present invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flow chart of a method for lossless compression of edge data of a mechanical vibration signal based on two-dimensional adaptive quantization according to the present invention;
FIG. 2 is a flow chart of adaptive quantization;
FIG. 3 is a plot of collected time domain data;
FIG. 4 is a graph of frequency domain data after orthogonal transformation;
FIG. 5 is a plot of positive two-dimensional frequency domain data;
fig. 6 is a diagram of quantization error data;
fig. 7 is a graph comparing compression rates of different compression methods.
Detailed Description
The following embodiments of the present invention are provided by way of specific examples, and other advantages and effects of the present invention will be readily apparent to those skilled in the art from the disclosure herein. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Wherein the showings are for the purpose of illustration only and not for the purpose of limiting the invention, shown in the drawings are schematic representations and not in the form of actual drawings; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not an indication or suggestion that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes, and are not to be construed as limiting the present invention, and the specific meaning of the terms may be understood by those skilled in the art according to specific situations.
As shown in fig. 1, a method for lossless compression of edge data of a mechanical vibration signal based on two-dimensional adaptive quantization includes the following steps:
s1: firstly, original time domain data is shown in fig. 3, an acquisition node located at the edge side of a network cuts acquired mechanical vibration signal data into blocks with a fixed length M through a sensor, and an original time domain two-dimensional data matrix X with the total number of blocks being L and the total length of original data being L × M is obtained:
s2: on an acquisition node at the edge side of the network, original time domain data is subjected to overlap orthogonal transformation (LOT) to convert the time domain data into frequency domain data, the subsequent processing process is facilitated by utilizing the characteristic of energy concentration of mechanical vibration signal data in the frequency domain, and the matrix form of the overlap orthogonal transformation is described as follows:
Y＝T'*X (1)
wherein Y is a frequency domain matrix, X is original two-dimensional time domain data, T is an orthogonal transformation matrix, T is a (L M) X (L M) order block diagonal matrix, and T' is a transpose matrix of T;
the conversion of the original data into the frequency domain means that if data is analyzed in the time domain of the mechanical vibration signal, the variation amplitude between adjacent data is relatively large and the variation rate is fast, making it difficult to compress the mechanical vibration signal data. After the orthogonal transformation method is used for processing, strong correlation exists in a frequency domain, and a strong energy accumulation characteristic is shown, so that an orthogonal transformation matrix W with the characteristic is selected. Further converting the raw data into the frequency domain.
Similar to the conventional orthogonal transformation, the overlapped orthogonal transformation divides the signal into L sections, but each section has a length of M1, and M < M1 ≦ 2M is satisfied, that is: there is signal overlap of length M1-M between two adjacent segments, the overlap orthogonal transformation still changes into coefficient vector with length M, so that the signal length in the changing domain is not changed, and the transformation matrix of LOT is set as:
wherein P is 0 For the M1xM order matrix, since only a segment of signal overlaps at the beginning and end of the signal, P needs to be defined separately 1 And P 2 (ii) a To ensure T L Are orthogonal, requiring P 0 Must be orthogonal, i.e.:
P′ 0 P 0 ＝I
at the same time, the overlap function of two adjacent segments must also satisfy orthogonality, i.e.:
P′ 0 WP 0 ＝P 0 WP′ 0 ＝0
wherein the transfer matrix W is:
wherein, I is M1-M order unit matrix, M1=2M is selected, therefore, the process of solving the frequency domain matrix Y through orthogonal variation in the formula (1) is written as the following form:
s3: as shown in fig. 4, the frequency domain matrix Y obtained after the orthogonal transformation is expressed as follows:
the invention adopts the overlapped orthogonal transformation because the overlapped orthogonal transformation has several characteristics which are superior to other changes, and the characteristics are as follows:
1) Entropy preservation: the Jacobin determinant with normalized orthogonal variation has a value of 1, which means that no information is lost by the orthogonal transformation itself, so that the information can be transmitted by using the transmission transformation coefficient
2) Energy conservation: and the two-dimensional Passevel theorem is satisfied, and the signal energy in the transform domain is equal to that in the original spatial domain. Thus, when the signal energy in the space domain is completely converted into a certain transform domain, the finite number of space sampling values can be completely recovered by the weighting of the finite number of transform coefficients to the base vector.
3) Decorrelation: orthogonal variation enables components of the vector signals to be uncorrelated, and a covariance matrix of the transform domain signals is a diagonal; under certain conditions (e.g., increasing transform size) the coefficients can even be made independent of each other, thus making the memorised source a memoryless source.
4) Energy redistribution and concentration: the most important feature of the orthogonal transformation is that the energy is mainly concentrated in the low frequency or low order region of the signal, making most of the transform coefficients zero or small. The bit with smaller energy can be discarded if the image quality allows, which is the root cause of the high data compression rate achieved by the orthogonal transformation.
5) If an orthogonal change exists, an inverse change must exist and the change is unique; the orthogonal change is simplest in calculation, if the orthogonal change is a discrete signal, and N is a finite value, the change is only simple matrix and vector operation, and the inverse change does not need inversion, so that the characteristic provides a condition for realizing the error calculation of the inverse orthogonal change under the condition that the storage space of the wireless sensor network node is limited.
6) The replacement of DCT with LOT is mainly based on the following two considerations: (1) The LOT is extremely similar to the DCT realization process, and the LOT quick algorithm is completed on the basis of the DCT quick algorithm; (2) The greatest advantage of LOT over DCT is that it can effectively remove blocking artifacts, thereby facilitating maximum compression of the data.
The coefficient matrix is then quantized using an adaptive quantization process. The quantization process shown is shown in fig. 2:
s4: in order to facilitate data compression and processing, values in the two-dimensional matrix Y are converted into positive values, positive and negative value information corresponding to the values in the Y is stored by using a P matrix, 1 in the P matrix is positive correspondingly, and-1 in the P matrix is negative correspondingly, and the converted positive two-dimensional frequency domain matrix is represented by B as shown in FIG. 5;
s5: the quantization degree is controlled by using a single-valued quantization bit number Q, L is the number of data segmentation blocks, M is the length of each block, Q represents the total number of the distributed quantization bit numbers, and the calculation mode of Q is as follows:
Q＝q*M*L (3)
s6: assigning a quantization bit for each value in the B matrix:
firstly, the positions of the first three corresponding maximum values in the positive two-dimensional frequency domain matrix B are found, and max _1, max _2and max _3are used for representing the maximum value, the second maximum value and the third maximum value respectively; dividing the value corresponding to the maximum value max _1 by 2 and comparing the divided value with max _2 and max _ 3; if max _1 is larger than max _2, modifying the value of the position (i, j) in B corresponding to max _ 1; if max _1 is smaller than max _2 and larger than max _3, modifying the value of the position (i, j) in B corresponding to max _1, and exchanging the values pointed by max _1 and max _2 to ensure that max _1 always points to the maximum value; if the value of max _1 is less than max _3, after modifying the corresponding value in the matrix B, pointing max _1 to max _2, pointing max \u2 to max _3, finding the third largest value in the matrix B and pointing it with max _ 3; every time the operation corresponding to the (i, j) position in the matrix is carried out, Q minus 1 operation is carried out on the total allocation position, the value corresponding to the (i, j) position in the quantization digit matrix Z (L x M) is increased by 1, and then a quantized matrix B and a quantization digit matrix Z are obtained;
max_1＝max_1/2 (4)
Q＝Q-1 (5)
B (i,j) ＝B (i,j) /2 (6)
Z (i,j) ＝Z (i,j) +1 (7)
s7: step S6 is repeated until all the quantization bits are allocated, i.e., the value of Q becomes 0, and Q quantization bits are allocated in total for the total number of coefficients, resulting in B (Q) and Z (Q).
S8: averaging the coefficient matrix B (Q) obtained after the last quantization, and storing the value as an average quantization step S;
s9: and calculating the maximum quantization value corresponding to each value in the original positive two-dimensional frequency domain matrix B according to the average quantization step S, wherein the calculation mode is as follows:
s10: calculating the maximum quantization bit value b corresponding to each value in the coefficient matrix max To obtain the maximum quantization bit matrix B max The calculation method is as follows:
s11: for lossless compression, a matrix B of maximum quantization bits is used max And the average quantization step S is used for inverse quantization to obtain inverse quantization momentThe matrix is calculated as follows:
s12: and carrying out inverse orthogonal transformation on the inverse quantization matrix to obtain a restored original matrix, wherein the calculation mode is as follows:
where P is the positive-negative value information indicated in step S4;
s13: and (3) solving errors with the original matrix, wherein an error matrix is represented by E, and as shown in FIG. 6, the obtained error matrix is as follows:
s14: using two-dimensional zero coding method to carry out error matrix E and maximum quantization bit matrix B max Coding is carried out, the zero counting coding mode is entered when the data 0 continuously appears to store the number of zero appearance, the zero counting coding mode is exited when the non-zero data is encountered to directly store, and the zero counting coding mode is obtained through the steps
And
the compression efficiency is greatly improved;
s15: considering the particularity of the positive and negative value information matrix P, since the matrix only has 1 and-1 data, 0 is used to replace-1; the binary representation method of bit coding, namely 0 and 1, namely data with the size of 1bit is adopted; the two-dimensional zero-coding method mentioned in step S14 is used to perform the consecutive 0 and 1 simultaneouslyCounting and storing the number of occurrences thereof, and obtaining the result through the step
And
s16: the transmission data is coded using a range coding method which first gives a sufficiently large range of integers and estimates of the probability of the occurrence of a symbol or number, the initial range being easily divided into sub-ranges whose size is proportional to the probability of the symbol they represent. Then, each symbol of the message is encoded in turn by reducing the current range to a sub-range that corresponds exactly to the next symbol to be encoded; will be provided with
After range coding, the data and S are put into a data stream as original data and are transmitted as compressed data;
s17: after the data center receives the data in the data stream, firstly, the data center is paired
Decoding according to two-dimensional zero code and bit code to obtain error data E and maximum quantization bit B max An orthogonal transformation matrix T and a positive and negative value information matrix P; and then, restoring the data according to the processes of the step S11 and the step S12, summing the obtained matrix and the error matrix E to obtain the original data, and realizing lossless compression and recovery of the data:
。
and step S5, when the total number of Q quantization digits is calculated, a quantization coefficient Q is used for operation, and the Q value is 0.856, so that lossless compression of data is realized.
In step S8, the average value of the coefficient matrix after the last quantization is selected as the quantization step S.
In step S11, before two-dimensional zero coding and bit coding, inverse orthogonal transformation and inverse quantization are carried out, and error calculation is carried out; error data E, orthogonal transformation matrix T, positive and negative value information matrix P and maximum quantization bit B max And zero counting and range coding can show better compression performance.
Figure 7 shows the compression ratio for different compression methods. From the results, the proposed lossless compression algorithm for the mechanical vibration signal edge data based on two-dimensional adaptive quantization is more effective, compared with the common compression software, such as 7-Zip, winRAR, zip and the like. The average compression rate of the two-dimensional block adaptively quantized mechanical vibration data lossless compression algorithm was 32.47%, while the average compression rate of the 7-Zip general compression software was 36.72%. This shows that the method can effectively improve the compression performance of the mechanical vibration data. The commercial compression software WinRAR has better performance in common application programs and performs worst. It only achieved a compression of 45.49% in the experiment. This also illustrates the need to design specific data compression algorithms for specific applications, such as lossless compression of mechanical vibration signal edge data.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.
Claims (3)
1. A lossless compression method for mechanical vibration signal edge data based on two-dimensional adaptive quantization is characterized in that: the method comprises the following steps:
s1: the method comprises the following steps that an acquisition node located on the edge side of a network cuts acquired mechanical vibration signal data into blocks in a fixed length M through a sensor, and an original time domain two-dimensional data matrix X with the total number of blocks being L is obtained, wherein the total length of original data is L M:
s2: on an acquisition node at the edge side of the network, performing overlapped orthogonal transformation on original time domain data to convert the time domain data into frequency domain data, wherein the matrix form of the overlapped orthogonal transformation is described as follows:
Y＝T'*X (1)
wherein Y is a frequency domain matrix, X is original two-dimensional time domain data, T is an orthogonal transformation matrix, T is a (L M) X (L M) order block diagonal matrix, and T' is a transpose matrix of T;
similar to the conventional orthogonal transformation, the overlapped orthogonal transformation divides the signal into L segments, but each segment has a length of M1, and M < M1 ≦ 2M is satisfied, that is: the adjacent two segments have signal overlap with length of M1-M, the overlapped orthogonal transformation is still changed into coefficient vector with length of M, so that the signal length on the change domain is not changed, and the transformation matrix of LOT is set as:
wherein P is 0 For M1xM order matrix, since only one segment of signal overlaps at the beginning and end of the signal, P needs to be defined separately 1 And P 2 (ii) a To ensure T L Are orthogonal, requiring P 0 Must be orthogonal, i.e.:
P′ 0 P 0 ＝I
at the same time, the overlap function of two adjacent segments must also satisfy orthogonality, i.e.:
P′ 0 WP 0 ＝P 0 WP′ 0 ＝0
wherein the transfer matrix W is:
wherein, I is M1-M order unit matrix, M1=2M is selected, therefore, the process of solving the frequency domain matrix Y through orthogonal variation in the formula (1) is written as the following form:
s3: the frequency domain matrix Y obtained after the orthogonal transformation is represented as follows:
s4: in order to facilitate data compression and processing, values in a two-dimensional matrix Y are converted into positive values, positive and negative value information corresponding to the values in the Y is stored by a P matrix, 1 in the P matrix is positive correspondingly, and-1 in the P matrix is negative correspondingly, and the converted positive two-dimensional frequency domain matrix is represented by B;
s5: the quantization degree is controlled by using a single-valued quantization bit Q, L is the number of data segmentation blocks, M is the length of each block, Q represents the total number of the distributed quantization bits, and the calculation mode of Q is as follows:
Q＝q*M*L (3)
s6: assign quantization bits for each value in the B matrix:
firstly, the positions of the first three corresponding maximum values in the positive two-dimensional frequency domain matrix B are found, and max _1, max _2and max _3are used for representing the maximum value, the second maximum value and the third maximum value respectively; dividing the value corresponding to the maximum value max _1 by 2 and comparing with max _2 and max _ 3; if max _1 is larger than max _2, modifying the value of the position (i, j) in B corresponding to max _ 1; if max _1 is smaller than max _2 and larger than max _3, modifying the value of the position (i, j) in B corresponding to max _1, and exchanging the values pointed by max _1 and max _2 to ensure that max _1 always points to the maximum value; if the value of max _1 is less than the value of max _3, after the corresponding value in the matrix B is modified, max _1 points to max _2, max _2points to max _3, and the third largest value is found in the matrix B and is pointed to the value by max _ 3; every time the operation corresponding to the (i, j) position in the matrix is carried out, Q minus 1 operation is carried out on the total allocation position, the value corresponding to the (i, j) position in the quantization digit matrix Z (L x M) is increased by 1, and then a quantized matrix B and a quantization digit matrix Z are obtained;
max_1＝max_1/2 (4)
Q＝Q-1 (5)
B (i,j) ＝B (i,j) /2 (6)
Z (i,j) ＝Z (i,j) +1 (7)
s7: repeating the step S6 until all quantization bits are allocated, namely the value of Q becomes 0, and Q quantization bits are allocated to the total number of coefficients to obtain B (Q) and Z (Q);
s8: averaging the coefficient matrix B (Q) obtained after the last quantization, and storing the value as an average quantization step S;
s9: and calculating the maximum quantization value corresponding to each value in the original positive two-dimensional frequency domain matrix B according to the average quantization step S, wherein the calculation mode is as follows:
s10: calculating the maximum quantization bit value b corresponding to each value in the coefficient matrix max To obtain the maximum quantization bit matrix B max The calculation method is as follows:
s11: for lossless compression, a matrix B of maximum quantization bits is used max And carrying out inverse quantization on the average quantization step S to obtain an inverse quantization matrix, wherein the calculation mode is as follows:
s12: and carrying out inverse orthogonal transformation on the inverse quantization matrix to obtain a restored original matrix, wherein the calculation mode is as follows:
where P is the positive-negative value information indicated in step S4;
s13: and solving errors with the original matrix, wherein the error matrix is represented by E, and the obtained error matrix is as follows:
s14: using two-dimensional zero coding method to carry out error matrix E and maximum quantization bit matrix B max Coding is carried out, the zero counting coding mode is entered when the data 0 continuously appears to store the number of zero appearance, the zero counting coding mode is exited when the non-zero data is encountered to directly store, and the zero counting coding mode is obtained through the steps
And
s15: considering the particularity of the positive and negative value information matrix P, since the matrix only has 1 and-1 data, 0 is used to replace-1; data with the size of 1bit is represented by binary system of 0 and 1 by adopting bit coding; meanwhile, the two-dimensional zero coding method mentioned in the step S14 is used for counting the continuous 0 and 1 and storing the occurrence times of the continuous 0 and 1, and the two-dimensional zero coding method is obtained through the step
And
s16: the transmission data are coded using a range coding method which firstly specifies a sufficiently large integer rangeAnd an estimate of the probability of the occurrence of a symbol or number, then encoding each symbol of the message in turn by reducing the current range to a sub-range corresponding exactly to the next symbol to be encoded; will be provided with
After range coding, the data and S are put into a data stream as original data and are transmitted as compressed data;
s17: after the data center receives the data in the data stream, firstly, the data center is paired
Decoding according to two-dimensional zero code and bit code to obtain error data E and maximum quantization bit B max An orthogonal transformation matrix T and a positive and negative value information matrix P; and then, restoring the data according to the processes of the step S11 and the step S12, summing the obtained matrix and the error matrix E to obtain the original data, and realizing lossless compression and recovery of the data:
2. the two-dimensional adaptive quantization-based mechanical vibration signal edge data lossless compression method according to claim 1, wherein: and step S5, when the total number of Q quantization digits is calculated, a quantization coefficient Q is used for operation, and the Q value is 0.856, so that lossless compression of data is realized.
3. The two-dimensional adaptive quantization-based lossless compression method for mechanical vibration signal edge data according to claim 1, wherein: s11, before two-dimensional zero coding and bit coding, inverse orthogonal transformation and inverse quantization are carried out, and error calculation is carried out; error data E, orthogonal transformation matrix T, positive and negative value information matrix P and maximum quantization bit B max Zero count and range coding are performed.
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