CN115774239B - Multi-target signal detection method based on non-uniform mutual mass array - Google Patents
Multi-target signal detection method based on non-uniform mutual mass array Download PDFInfo
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Abstract
The invention relates to a multi-target signal detection method based on a non-uniform mutual mass array, which comprises the following steps: s1, detecting narrowband signals of different frequency bands in a sound source total signal; s2, if the number of the narrow-band signals is smaller than or equal to the number of the uniform linear arrays in the non-uniform mutual mass linear arrays, performing a step S3, otherwise, ending the detection; s3, adjusting the intervals among array elements in the plurality of detection line arrays based on the wavelength of the center frequency of each narrowband signal so that the main imaging frequency of the plurality of detection line arrays is consistent with the center frequency of the plurality of narrowband signals respectively; and S4, calculating one or more target signal angles detected by the detection line array at the main imaging frequency based on the sound source total signals received by the detection line array, the position coordinates of each array element in the detection line array, the main imaging frequency of the detection line array and the azimuth arrival angle estimation model. The invention introduces non-uniform mutual mass arrays capable of detecting a plurality of frequency points, and each uniform array can detect and obtain corresponding target signal angles at the main imaging frequency.
Description
Technical Field
The invention belongs to the technical field of multi-signal detection, and particularly relates to a multi-target signal detection method based on a non-uniform mutual mass array.
Background
In living and production environments, most of airtight pipelines or containers are leaked for various reasons, so that the leakage not only causes waste and economic loss of resources, but also causes serious safety problems due to leakage of harmful flammable and explosive gases or liquids, and therefore, many methods for effectively detecting the leakage have been applied for many years. When any pressure gas leaks or vacuum leaks, the gas flow forms turbulence, the turbulence emits sound wave energy, and sound waves cover the audible range and the ultrasonic frequency range. In a general environment, noisy ambient noise is very easy to mask the acoustic wave signal in the audible domain. The device will typically detect its ultrasonic frequency band.
Conventional detection devices are typically based on microphone arrays, detecting at ultrasonic frequency bands of no more than 50 kHz. Microphone arrays typically employ uniform line arrays and planar arrays, as well as non-uniform arrays, mostly sparse line arrays or planar arrays. The area array is generally a circular aperture array, a rectangular array of grids, a regular polygon array, or the like. Based on the microphone pickup array formed by the arrays, bandpass or high-pass filtering effects can be generated on specific frequency points or frequency bands, and the interference superposition is used for enhancing the directional and fixed-frequency pickup capability of the microphone pickup array, so that leakage abnormal sound is extracted. This has the advantage that a stronger and more accurate leak detection capability may be provided for a particular frequency bin of a single target. However, in the actual situation with multiple leakage targets and multiple leakage signal characteristic frequency points, the conventional detection means is used for detecting that the imaging of the system is interfered, and erroneous imaging is generated or misjudgment about whether leakage occurs is generated.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a multi-target signal detection method based on a non-uniform mutual mass array, which can realize multi-target leakage signal detection and imaging by utilizing incoherent multi-frequency points. The invention adopts the following technical scheme:
a multi-target signal detection method based on a non-uniform mutual mass array comprises the following steps:
s1, detecting a sound source total signal based on a non-uniform mutual linear array, and detecting narrowband signals of different frequency bands in the sound source total signal, wherein the non-uniform mutual linear array consists of a plurality of uniform linear arrays, and the number of array elements in each uniform linear array is recorded as
,/>
All of them are mutually equal in nature and are treated by>
Representing the number of uniform linear arrays;
s2, if the number of the narrow-band signals is smaller than or equal to the number of the uniform linear arrays in the non-uniform mutual mass linear arrays, performing a step S3, otherwise ending detection;
s3, selecting a plurality of uniform linear arrays with the same quantity as the narrow-band signals from the non-uniform mutual linear arrays to serve as the linear arrays for detecting the multi-target signals, and adjusting each array element in the plurality of linear arrays based on the wavelength of the center frequency of each narrow-band signalThe distance between the two arrays is set so that the main imaging frequency of the arrays is consistent with the central frequency of the narrow-band signals, and the distance between array elements in each array is recorded as
And->
All of them are mutually equal in nature and are treated by>
Representing the number of the detection line arrays; />
S4, establishing an azimuth arrival angle estimation model, and calculating one or more target signal angles detected by the detection line array at the main imaging frequency of the detection line array according to the total sound source signals received by the detection line array, the position coordinates of each array element in the detection line array, the main imaging frequency of the detection line array and the azimuth arrival angle estimation model;
s5, detecting the multi-target signal based on the target signal angles detected by the detection line arrays at the main imaging frequency of the detection line arrays.
In a preferred embodiment, in step S4, the azimuth angle of arrival estimation model is specifically:
suppose for the first
The incidence angles of the target signals detected by the detection line arrays are respectively
，/>
Indicate->
The detection of the individual detection lines +.>
Incidence angle of the individual target signals, +.>
The number of target signals is represented by:
wherein ,
indicate->
The total signal of sound sources detected by the individual detection line arrays, < >>
Vector matrix representing each target signal, +.>
Indicate->
The phase difference matrix of each target signal in each detection line array reaching each array element is +.>
Indicate->
Complex-vector gaussian white noise detected by the detection line arrays;
wherein ,
indicate->
The first line of detection>
A phase difference matrix of the target signals reaching each array element based on the +.>
Position coordinates of each array element in each detection line array +.>
Main imaging frequencies of the detection line arrays are obtained through calculation;
for the first
Covariance matrix of cross matrix is calculated by sound source total signal detected by each detection line array>
：
wherein ,
representing the desired value>
Represents the conjugate transpose->
，/>
Representing noise signal power, < >>
Representing the identity matrix;
for a pair of
Performing eigenvalue decomposition to obtain:
wherein ,
representing feature vectors +_>
Representing the feature vector;
will be
The signal space and the noise space are decomposed to obtain:
wherein ,
representing feature vectors in signal space, +.>
Representing feature vectors in signal space, +.>
Representing feature vectors in noise space, +.>
Representing feature vectors in noise space; />
Based on the formula
Calculating to obtain the qualified +.>
Eligible->
Namely +.>
The individual linear arrays detect the resulting target signal angle at their primary imaging frequency.
As a preferable scheme:
wherein ,
indicate->
Vector of individual target signals,/>
Representing the transpose.
As a preferable scheme:
wherein ,
indicate->
The first line of detection>
The target signal reaches the->
Phase difference between each element and the first element is reached,/->
Indicate->
The>
Position coordinates of individual array elements,/->
Indicate->
Personal examinationThe number of array elements in the linear array, +.>
，/>
Representing sound speed,/->
Indicate->
The main imaging frequency of each of the linear arrays.
In step S4, for any one of the detection line arrays, one or more target signal angles detected by the detection line array at a plurality of secondary primary imaging frequencies thereof are calculated based on the total sound source signal received by the detection line array, the position coordinates of each array element in the detection line array, a plurality of secondary primary imaging frequencies of the detection line array, and an azimuth arrival angle estimation model, wherein the plurality of secondary primary imaging frequencies are all within a preset range up and down with respect to the center frequency of the narrowband signal corresponding to the detection line array.
Preferably, between step S4 and step S5, step B is further included:
B. for the same detection line array, filtering target signals received at a plurality of imaging frequencies and at different target signal angles, wherein the filtering process comprises the following steps:
b1, calculating the intensity of target signals of the detection line array at one or more target signal angles received at a main imaging frequency, and the intensity of target signals of the detection line array at one or more target signal angles received at a secondary main imaging frequency;
and B2, if the difference value between the intensity of the target signal at the corresponding target signal angle received at the secondary main imaging frequency and the intensity of the strongest target signal received at the main imaging frequency is larger than a preset sound intensity difference threshold value, filtering the target signal at the corresponding target signal angle received at the secondary main imaging frequency.
Preferably, the intensity calculation formula of the target signal is:
wherein ,
is expressed in the imaging frequency +.>
The angle of the target signal received at the receiver is +.>
The strength of the target signal at that location.
Preferably, step a is further included between step S4 and step S5:
A. judging whether a difference value between two target signal angles is smaller than a preset threshold value degree or not among the plurality of target signal angles, if so, considering that the two target signal angles correspond to the same target signal, and calculating the target signal based on the average value of the two target signal angles to obtain the final corresponding target signal angle.
Preferably, the preset threshold degree is 5 °.
In step S3, the spacing between the array elements in the detection line array is half the wavelength of the center frequency of the narrowband signal corresponding to the spacing.
The beneficial effects of the invention are as follows:
and a non-uniform mutual mass array capable of detecting a plurality of frequency points is introduced, and compared with a traditional linear array and an area array of a microphone, each uniform array in the non-uniform mutual mass array can be detected at a main imaging frequency to obtain a corresponding target signal angle, so that estimation errors of arrival angles caused by a plurality of signal source gas leakage points can not occur.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a multi-target signal detection method based on a non-uniform mutual mass array according to the present invention;
FIG. 2 is a schematic diagram of a non-uniform mutual mass array according to the present invention.
Detailed Description
The following specific examples are presented to illustrate the present invention, and those skilled in the art will readily appreciate the additional advantages and capabilities of the present invention as disclosed herein. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the following embodiments and features in the embodiments may be combined with each other without conflict.
Referring to fig. 1, the embodiment provides a multi-target signal detection method based on a non-uniform mutual mass array, which includes the steps of:
s1, detecting a sound source total signal based on a non-uniform mutual linear array, and detecting narrowband signals of different frequency bands in the sound source total signal, wherein the non-uniform mutual linear array consists of a plurality of uniform linear arrays, and the number of array elements in each uniform linear array is recorded as
,/>
All of them are mutually equal in nature and are treated by>
Representing the number of uniform linear arrays.
S2, if the number of the narrow-band signals is smaller than or equal to the number of the uniform linear arrays in the non-uniform mutual mass linear arrays, performing step S3, otherwise ending detection.
Because the number of the narrow-band signals is larger than the number of the uniform linear arrays in the non-uniform mutual linear array and exceeds the number of main imaging frequencies which can be provided by the non-uniform mutual linear array, the final multi-target signal detection precision can be reduced, and therefore the situation that the number of the narrow-band signals is larger than the number of the uniform linear arrays in the non-uniform mutual linear array is not considered in the embodiment.
S3, randomly selecting a plurality of uniform linear arrays with the same number as the narrow-band signals from the non-uniform mutual linear arrays to serve as the linear arrays for detecting the multi-target signals, and adjusting the intervals among the array elements in the plurality of the linear arrays based on the wavelength of the central frequency of each narrow-band signal (the adjustment of the positions of the array elements is needed to be explained here can be realized through a position adjusting device) so that the main imaging frequencies of the plurality of the linear arrays are respectively consistent with the central frequency of the plurality of narrow-band signals, wherein the intervals among the array elements in the plurality of the linear arrays are recorded as
And->
All of them are mutually equal in nature and are treated by>
Representing the number of the detection lines.
The main imaging frequencies of the plurality of the detection line arrays are respectively consistent with the center frequencies of the plurality of the narrowband signals, and the intervals among the array elements in the detection line arrays are half of the wavelengths of the center frequencies of the narrowband signals corresponding to the intervals.
Referring to fig. 2, a non-uniform mutual linear array formed by two uniform linear arrays is shown, and because the number of array elements and the spacing between the array elements are all of the same mass, when the array elements are on a straight line, only the first array element of the two uniform linear arrays can be overlapped.
S4, an azimuth arrival angle estimation model is established, and for any detection line array, one or more target signal angles (to be noted, one or more target signal angles detected at the main imaging frequency may exist in the target signal angles detected at the main imaging frequency) of the detection line array are obtained through calculation based on the total sound source signals received by the detection line array, the position coordinates of each array element in the detection line array, the main imaging frequency of the detection line array and the azimuth arrival angle estimation model (to be explained specifically below).
S5, detecting the multi-target signal based on the target signal angles detected by the detection line arrays at the main imaging frequency, and performing final imaging.
It should be noted that, in this embodiment, the number of target signals is generally less than 4, otherwise, the scale of the heterogeneous linear array will be too large, and it is difficult to obtain a realistic array.
Therefore, the invention introduces the non-uniform mutual mass array capable of detecting a plurality of frequency points, and compared with the traditional linear array and the area array of the microphone, each uniform array in the non-uniform mutual mass array can detect and obtain a corresponding target signal angle at the main imaging frequency, and the estimation error of the arrival angle caused by a plurality of signal source gas leakage points can not occur.
Specifically:
when in far field
The target signals have different frequency bands +.>
The narrow-band signals are respectively->
The receiving of the detection line array is realized by different line array gating when continuous signal sampling is carried out at equal time intervals, and the time intervals are +.>
A certain group of uniform linear arrays is strobed in turn.
In step S4, the azimuth angle of arrival estimation model specifically includes:
suppose for the first
The incidence angles of the target signals detected by the detection line arrays are respectively
，/>
Indicate->
The detection of the individual detection lines +.>
Incidence angle of the individual target signals, +.>
The number of target signals is represented by:
wherein ,
indicate->
The total signal of sound sources detected by the individual detection line arrays, < >>
Vector matrix representing each target signal, +.>
Indicate->
The phase difference matrix of each target signal in each detection line array reaching each array element is +.>
Indicate->
Complex vector gaussian white noise detected by each detection line array.
wherein ,
indicate->
Vector of individual target signals,/>
Representing the transpose. />
wherein ,
indicate->
The first line of detection>
A phase difference matrix of the target signals reaching each array element based on the +.>
Position coordinates of each array element in each detection line array +.>
And calculating the main imaging frequency of each detection line array.
wherein ,
indicate->
The first line of detection>
The target signal reaches the->
Phase difference between each element and the first element is reached,/->
Indicate->
The>
Position coordinates of individual array elements,/->
Indicate->
The number of array elements in each detection line array, +.>
，/>
Representing the sound velocity, 340m/s in this embodiment, a more accurate value may be used in the actual value, and +.>
Indicate->
The main imaging frequency of each of the linear arrays.
For the first
Covariance matrix of cross matrix is calculated by sound source total signal detected by each detection line array>
：
wherein ,
representing the desired value>
Represents the conjugate transpose->
，/>
Representing noise signal power, < >>
Representing the identity matrix.
For a pair of
Performing eigenvalue decomposition to obtain:
wherein ,
representing feature vectors +_>
Representing the feature vector.
Will be
The signal space and the noise space are decomposed to obtain:
wherein ,
representing feature vectors in signal space, +.>
Representing feature vectors in signal space, +.>
Representing feature vectors in noise space, +.>
Representing the feature vector in noise space.
Based on the formula
Calculating to obtain the qualified +.>
Eligible->
Namely +.>
The individual linear arrays detect the resulting target signal angle at their primary imaging frequency.
Here, the formula is satisfied
There may be a plurality of target signal angles and thus there may be a plurality of target signal angles detected at the primary imaging frequency.
In the actual operation process, the formula is as follows
Can be adjusted to->
Only the formula->
As far as possible, 0, a range can be given in which the angles are all solved.
And calculating target signal angles obtained by detecting the other detection line arrays at the respective main imaging frequencies sequentially based on the azimuth arrival angle estimation model, thus finishing multi-target signal detection and carrying out final imaging.
In this embodiment, in step S4, for any one of the detection line arrays, one or more target signal angles (similarly, a plurality of target signal angles may be detected at a secondary primary imaging frequency) detected by the detection line array at a plurality of secondary primary imaging frequencies are also calculated based on the total sound source signal received by the detection line array, the position coordinates of each array element in the detection line array, the plurality of secondary primary imaging frequencies of the detection line array, and the azimuth arrival angle estimation model, where the plurality of secondary primary imaging frequencies are all within a preset range above and below the center frequency of the narrowband signal corresponding to the detection line array.
That is, in this embodiment, for any one of the detection line arrays, a plurality of secondary primary imaging frequencies are also taken within the upper and lower preset ranges of the primary imaging frequencies, and the calculation of the azimuth arrival angle estimation model is repeatedly performed to calculate the target signal angles detected by the detection line array at the plurality of secondary primary imaging frequencies (it should be noted that, when the secondary primary imaging frequencies are adopted for calculation, the above formula is given in the following manner
And (3) replacing the value of the (c) and other calculation steps are consistent). The beneficial effects of this operation procedure are: image frequency points are added, and errors caused by physical positions of the array are eliminated.
After the step S4 is performed, a plurality of target signal angles may be obtained, and when the target signal angles corresponding to the plurality of target signals have a certain large angular resolution (generally greater than or equal to 5 °), multi-target multi-frequency point imaging may be achieved. If the signal is smaller than 5 °, the two target signals are considered to be the same target signal, so step a is further included between step S4 and step S5:
A. judging whether a difference value between two target signal angles is smaller than a preset threshold value degree or not among the plurality of target signal angles, if so, considering that the two target signal angles correspond to the same target signal, and calculating the target signal based on the average value of the two target signal angles to obtain the final corresponding target signal angle.
Finally, between step S4 and step S5, step B is further included:
B. for the same detection line array, filtering target signals received at a plurality of imaging frequencies and at different target signal angles, wherein the filtering process comprises the following steps:
b1, calculating the intensity of target signals of the detection line array at one or more target signal angles received at a main imaging frequency, and the intensity of target signals of the detection line array at one or more target signal angles received at a secondary main imaging frequency;
and B2, if the difference value between the intensity of the target signal at the corresponding target signal angle received at the secondary main imaging frequency and the intensity of the strongest target signal received at the main imaging frequency is larger than a preset sound intensity difference threshold (the sound intensity difference threshold is set to be 12dB in the embodiment), filtering the target signal at the corresponding target signal angle received at the secondary main imaging frequency.
The beneficial effects of this operation procedure are: interference noise is eliminated, so that the actual sound source localization is more obvious.
The intensity calculation formula of the target signal is:
wherein ,
is expressed in the imaging frequency +.>
The angle of the target signal received at the receiver is +.>
The strength of the target signal at that location.
The above examples are merely illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention, and various modifications and improvements made by those skilled in the art to the technical solution of the present invention should fall within the protection scope of the present invention without departing from the design spirit of the present invention.
Claims (10)
1. A multi-target signal detection method based on a non-uniform mutual mass array is characterized by comprising the following steps:
s1, detecting a sound source total signal based on a non-uniform mutual linear array, and detecting narrowband signals of different frequency bands in the sound source total signal, wherein the non-uniform mutual linear array consists of a plurality of uniform linear arrays, and the number of array elements in each uniform linear array is recorded as
,/>
All of them are mutually equal in nature and are treated by>
Representing the number of uniform linear arrays;
s2, if the number of the narrow-band signals is smaller than or equal to the number of the uniform linear arrays in the non-uniform mutual mass linear arrays, performing a step S3, otherwise ending detection;
s3, selecting a plurality of uniform linear arrays with the same number as the narrow-band signals from the non-uniform mutual linear arrays to serve as the linear arrays for detecting the multi-target signals, and adjusting the intervals among the array elements in the plurality of the linear arrays based on the wavelength of the central frequency of each narrow-band signal, so that the main imaging frequency of the plurality of the linear arrays is respectively consistent with the central frequency of the plurality of the narrow-band signals, and the array element intervals in the plurality of the linear arrays are recorded as
And->
All betweenMutual mass (I/II)>
Representing the number of the detection line arrays;
s4, establishing an azimuth arrival angle estimation model, and calculating one or more target signal angles detected by the detection line array at the main imaging frequency of the detection line array according to the total sound source signals received by the detection line array, the position coordinates of each array element in the detection line array, the main imaging frequency of the detection line array and the azimuth arrival angle estimation model;
s5, detecting the multi-target signal based on the target signal angles detected by the detection line arrays at the main imaging frequency of the detection line arrays.
2. The method for detecting multi-target signals based on the non-uniform mutual mass array according to claim 1, wherein in step S4, the azimuth angle of arrival estimation model is specifically:
suppose for the first
The incidence angles of the target signals detected by the detection line arrays are respectively
，/>
Indicate->
The detection of the individual detection lines +.>
Incidence angle of the individual target signals, +.>
The number of target signals is represented by:
wherein ,
indicate->
The total signal of sound sources detected by the individual detection line arrays, < >>
Vector matrix representing each target signal, +.>
Indicate->
The phase difference matrix of each target signal in each detection line array reaching each array element is +.>
Represent the first
Complex-vector gaussian white noise detected by the detection line arrays;
wherein ,
indicate->
The first line of detection>
A phase difference matrix of the target signals reaching each array element based on the +.>
Position coordinates of each array element in each detection line array +.>
Main imaging frequencies of the detection line arrays are obtained through calculation;
for the first
Covariance matrix of cross matrix is calculated by sound source total signal detected by each detection line array>
：
wherein ,
representing the desired value>
Represents the conjugate transpose->
，/>
Representing noise signal power, < >>
Representing the identity matrix;
for a pair of
Performing eigenvalue decomposition to obtain:
wherein ,
feature vector representing total signal of sound source, +.>
A diagonal matrix representing the composition of the eigenvalues;
will be
The signal space and the noise space are decomposed to obtain:
wherein ,
representing feature vectors in signal space, +.>
Representing a diagonal matrix under signal space, +.>
Representing feature vectors in noise space, +.>
Representing a diagonal matrix under noise space;
based on the formula
Calculating to obtain the qualified +.>
Eligible->
Namely +.>
The individual linear arrays detect the resulting target signal angle at their primary imaging frequency.
3. The multi-target signal detection method based on the non-uniform mutual mass array according to claim 2, wherein the method is characterized in that:
wherein ,
indicate->
Vector of individual target signals,/>
Representing the transpose.
4. The multi-target signal detection method based on the non-uniform mutual mass array according to claim 2, wherein the method is characterized in that:
wherein ,
indicate->
The first line of detection>
The target signal reaches the->
Phase difference between each element and the first element is reached,/->
Indicate->
The>
Position coordinates of individual array elements,/->
Indicate->
The number of array elements in each detection line array, +.>
，/>
Representing sound speed,/->
Indicate->
The principal imaging frequency of each of the linear arrays, j, represents an imaginary unit.
5. The method for detecting multiple target signals based on non-uniform mutual mass arrays according to claim 4, wherein in step S4, for any one of the detection line arrays, one or more target signal angles detected by the detection line array at a plurality of secondary primary imaging frequencies thereof are calculated based on a sound source total signal received by the detection line array, position coordinates of each array element in the detection line array, a plurality of secondary primary imaging frequencies of the detection line array and an azimuth arrival angle estimation model, and the plurality of secondary primary imaging frequencies are all within a preset range up and down with respect to a center frequency of a narrowband signal corresponding to the detection line array.
6. The method for detecting multiple target signals based on non-uniform mutual mass array according to claim 5, wherein between step S4 and step S5, further comprising step B:
B. for the same detection line array, filtering target signals received at a plurality of imaging frequencies and at different target signal angles, wherein the filtering process comprises the following steps:
b1, calculating the intensity of target signals of the detection line array at one or more target signal angles received at a main imaging frequency, and the intensity of target signals of the detection line array at one or more target signal angles received at a secondary main imaging frequency;
and B2, if the difference value between the intensity of the target signal at the corresponding target signal angle received at the secondary main imaging frequency and the intensity of the strongest target signal received at the main imaging frequency is larger than a preset sound intensity difference threshold value, filtering the target signal at the corresponding target signal angle received at the secondary main imaging frequency.
7. The method for detecting multiple target signals based on the non-uniform mutual mass array according to claim 6, wherein the intensity calculation formula of the target signals is:
wherein ,
is expressed in the imaging frequency +.>
The angle of the target signal received at the receiver is +.>
The strength of the target signal at that location.
8. The method for detecting multiple target signals based on non-uniform mutual mass array according to claim 1, wherein step a is further included between step S4 and step S5:
A. judging whether a difference value between two target signal angles is smaller than a preset threshold value degree or not among the plurality of target signal angles, if so, considering that the two target signal angles correspond to the same target signal, and calculating the target signal based on the average value of the two target signal angles to obtain the final corresponding target signal angle.
9. The method for detecting multiple target signals based on a non-uniform mutual mass array according to claim 8, wherein the preset threshold degree is 5 °.
10. The method for detecting multiple target signals based on non-uniform mutual mass arrays according to claim 1, wherein in step S3, the spacing between each array element in the detection line array is half the wavelength of the center frequency of the narrowband signal corresponding to the spacing.
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