CN116087435B - Air quality monitoring method, electronic equipment and storage medium - Google Patents

Air quality monitoring method, electronic equipment and storage medium Download PDF

Info

Publication number
CN116087435B
CN116087435B CN202310347881.3A CN202310347881A CN116087435B CN 116087435 B CN116087435 B CN 116087435B CN 202310347881 A CN202310347881 A CN 202310347881A CN 116087435 B CN116087435 B CN 116087435B
Authority
CN
China
Prior art keywords
tensor
data
air quality
factor matrix
updated
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202310347881.3A
Other languages
Chinese (zh)
Other versions
CN116087435A (en
Inventor
符蕴芳
张艮山
宋保平
陈永肖
符瑞毅
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Hebei Linghe Computer Information Technology Co ltd
Original Assignee
Shijiazhuang University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shijiazhuang University filed Critical Shijiazhuang University
Priority to CN202310347881.3A priority Critical patent/CN116087435B/en
Publication of CN116087435A publication Critical patent/CN116087435A/en
Application granted granted Critical
Publication of CN116087435B publication Critical patent/CN116087435B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N33/00—Investigating or analysing materials by specific methods not covered by groups G01N1/00 - G01N31/00
    • G01N33/0004—Gaseous mixtures, e.g. polluted air
    • G01N33/0009—General constructional details of gas analysers, e.g. portable test equipment
    • G01N33/0062—General constructional details of gas analysers, e.g. portable test equipment concerning the measuring method, e.g. intermittent, or the display, e.g. digital
    • G01N33/0067—General constructional details of gas analysers, e.g. portable test equipment concerning the measuring method, e.g. intermittent, or the display, e.g. digital by measuring the rate of variation of the concentration
    • G01N33/0068—
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis

Abstract

The invention provides an air quality monitoring method, electronic equipment and a storage medium, wherein air quality data of a to-be-detected point are firstly obtained to construct tensor data; then performing Tucker decomposition on the tensor data to obtain a kernel tensor and a factor matrix corresponding to each mode; then combining with the tensor complement model, solving the model by adopting an optimization minimization method to obtain a reconstruction tensor; the tensor complement model is provided with a kernel norm and a log-sum penalty function to reflect the low rank property of a factor matrix corresponding to each module and the structural sparsity of the kernel tensor; and then, according to the reconstruction tensor, supplementing tensor data of the detection point to obtain the supplemented tensor data, thereby determining the air quality monitoring result of the detection point. The reconstruction tensor is constructed through the low-rank structure of the factor matrix corresponding to each module generated by decomposition and the structural sparsity of the nuclear tensor, so that the low-rank property among the dimensions of tensor data is described, the tensor data is complemented, and the accurate monitoring of air quality is realized.

Description

Air quality monitoring method, electronic equipment and storage medium
Technical Field
The invention belongs to the technical field of pollution monitoring, and particularly relates to an air quality monitoring method, electronic equipment and a storage medium.
Background
With the progress of urban and industrial, the problem of environmental air pollution is receiving more and more public attention. Because the environmental air pollution is an important environmental pollution source affecting the health of residents, the situation of treating the atmospheric pollution, improving the air quality, strengthening the scientific prevention and control of the atmospheric pollution and promoting the green development is promoted.
In order to monitor the air quality, air quality monitoring stations are provided in many areas. Air quality monitoring stations typically implement grid-like monitoring by acquiring spatial data of the integrity of the monitored area. However, at present, sparse air quality monitoring stations can only cover a certain monitoring area and cannot cover a city completely, so that the actual air pollutant spatial distribution mechanism and the time-varying characteristic of pollutant concentration are difficult to reflect, and the effect of air quality monitoring is poor.
Disclosure of Invention
In view of the above, the present invention provides an air quality monitoring method, an electronic device and a storage medium, which aim to solve the problem of poor air quality monitoring effect in the prior art.
A first aspect of an embodiment of the present invention provides an air quality monitoring method, including:
acquiring air quality data of a to-be-detected point, and constructing tensor data of the to-be-detected point according to the air quality data;
performing Tucker decomposition on the tensor data to obtain a kernel tensor and a factor matrix corresponding to each mode;
inputting the nuclear tensor, factor matrixes corresponding to all modes and tensor data into a pre-established tensor completion model, and solving the tensor completion model by adopting an optimization minimization method to obtain a reconstruction tensor; the tensor complement model is provided with a kernel norm and a log-sum penalty function; the kernel norm is used for representing low-rank log-sum penalty functions of factor matrixes corresponding to all modes and is used for processing the structural sparsity of the kernel tensor;
according to the reconstruction tensor, supplementing tensor data of the detection point to obtain supplemented tensor data;
and determining an air quality monitoring result of the to-be-detected point according to the tensor data after the completion.
A second aspect of an embodiment of the present invention provides an air quality monitoring device, including:
the acquisition module is used for acquiring air quality data of the to-be-detected points and constructing tensor data of the to-be-detected points according to the air quality data;
the decomposition module is used for performing Tucker decomposition on the tensor data to obtain a kernel tensor and a factor matrix corresponding to each mode;
the reconstruction module is used for inputting the nuclear tensor, the factor matrix corresponding to each module and tensor data into a pre-established tensor completion model, and solving the tensor completion model by adopting an optimization minimization method to obtain a reconstruction tensor; the tensor complement model is provided with a kernel norm; the kernel norm is used for representing the low rank property of the factor matrix corresponding to each module; meanwhile, a log-sum penalty function is also arranged for processing the sparsity of the nuclear tensor structure;
the complementing module is used for complementing the tensor data of the detection points according to the reconstruction tensor to obtain the complemented tensor data;
and the determining module is used for determining an air quality monitoring result of the to-be-detected point according to the tensor data after the completion.
A third aspect of an embodiment of the invention provides an electronic device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, the processor implementing the steps of the air quality monitoring method of the first aspect above when the computer program is executed.
A fourth aspect of an embodiment of the invention provides a computer readable storage medium storing a computer program which when executed by a processor performs the steps of the air quality monitoring method of the first aspect above.
According to the air quality monitoring method, the electronic equipment and the storage medium provided by the embodiment of the invention, firstly, air quality data of a to-be-detected point is obtained, and tensor data of the to-be-detected point is constructed according to the air quality data; then performing Tucker decomposition on the tensor data to obtain a kernel tensor and a factor matrix corresponding to each mode; inputting the nuclear tensor, the factor matrix corresponding to each mode and tensor data into a pre-established tensor complement model, and solving the tensor complement model by adopting an optimization minimization method to obtain a reconstruction tensor; the tensor complement model is provided with a kernel norm; the kernel norm is used for representing the low rank property of the factor matrix corresponding to each module; meanwhile, a log-sum penalty function is also arranged for processing the sparsity of the nuclear tensor structure; then, according to the reconstruction tensor, supplementing tensor data of the detection point to obtain supplemented tensor data; and finally, determining an air quality monitoring result of the to-be-detected point according to the tensor data after the completion. The reconstruction tensor is constructed through the low-rank structure of the factor matrix corresponding to each module generated by decomposing the tensor data and the structural sparsity of the nuclear tensor, so that the low-rank property among the dimensions of the tensor data is described, the tensor data is complemented, and the accurate monitoring of the air quality is realized.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments or the description of the prior art will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present 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 an application scenario diagram of an air quality monitoring method provided by an embodiment of the present invention;
FIG. 2 is a flow chart of an implementation of the air quality monitoring method provided by the embodiment of the invention;
FIG. 3 is a flow chart of an implementation of a method for air quality monitoring according to another embodiment of the present invention;
FIG. 4 is a schematic diagram of an air quality monitoring device according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth such as the particular system architecture, techniques, etc., in order to provide a thorough understanding of the embodiments of the present invention. It will be apparent, however, to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.
In the prior art, air quality space data of the whole city plane is generally obtained by using a space interpolation algorithm, so that the resolution of air quality monitoring is effectively improved. The algorithms are mainly divided into three types, one type is a statistical algorithm, and the statistical algorithm comprises kriging interpolation, inverse distance weighting and the like; the second category is a machine learning algorithm, including random forests, multi-layer perceptrons, neural networks, and the like; the third class is by means of tensor representation algorithms.
The correlation of distance and air pollutant concentration is a basic assumption of a statistical algorithm, and the simple assumption cannot well reflect the mechanism of air pollutant spatial distribution, and often cannot consider the time-varying characteristics of air pollutant concentration.
The machine learning algorithm may combine the historical concentrations of air pollutants and fuse multiple air pollutant concentrations to increase the spatial resolution of the air pollutant concentrations. However, as the machine learning algorithm focuses on fitting data and the non-intuitive internal mechanism thereof, the calculation complexity in the machine learning model is higher, and the history data of the air pollutants combined by the machine learning algorithm is often simply input as a model, the time-varying rule of the air pollutants cannot be directly described, so that the two problems of improving the spatial resolution of the air pollutant concentration and analyzing the time-varying characteristic of the air pollutant concentration are mutually independent.
The tensor-based representation algorithm firstly represents the spatial distribution of an air quality monitoring station, the time sequence of the pollutant concentration and the pollutant concentration by tensor data, then constructs a tensor complement optimization problem, then adopts a tensor singular value decomposition iterative updating algorithm to solve the problem, finally obtains singular vectors after singular value decomposition to complement the tensor data, and adopts an evaluation index to evaluate the tensor data after tensor complement. The method effectively solves the problems of the first type and the second type, fuses multi-source data and space-time air pollutant concentration data to perform tensor complementation, and obtains high-precision tensor data to obtain better spatial resolution.
However, the tensor representation algorithm described above does not sufficiently consider the low rank property of the spatial tensor data of the monitored region based on tensor representation, and has a problem of high accuracy of tensor data after tensor complementation, and thus has poor air quality monitoring effect.
The invention provides an air quality monitoring method, which is characterized in that on the basis of the tensor expression algorithm, a reconstruction tensor is constructed through the low-rank structure of a factor matrix generated by decomposition and the structural sparsity of a nuclear tensor, so that the low-rank property among each dimension of tensor data is depicted, the tensor data is complemented, and the accurate monitoring of the air quality is realized.
Fig. 1 is an application scenario diagram of an air quality monitoring method provided by an embodiment of the present invention. As shown in fig. 1, in some embodiments, the air quality monitoring method provided in the embodiments of the present invention may be applied to, but not limited to, the application scenario. In an embodiment of the invention, the system comprises: an air quality monitoring station 11 and an electronic device 12.
Wherein, a plurality of sensors are arranged in the air quality monitoring station 11 and are used for measuring PM2.5, PM10 and O 3 、SO 2 、NO 2 Air quality data such as CO, temperature, air pressure, humidity, wind direction, wind speed, etc. The electronic device 12 may be a terminal or a server, and the terminal may be a single-chip microcomputer, a computer, or the like, which is not limited herein. The server may be a physical server, a cloud server, etc., and is not limited herein. The electronic device 12 may be disposed in the air quality monitoring station 11, and may process air quality data of a single air quality monitoring station 11, or may communicate with a plurality of air quality monitoring stations 11, and process air quality data of a plurality of air quality monitoring stations 11 in a certain area, which is not limited herein.
Fig. 2 is a flowchart of an implementation of an air quality monitoring method according to an embodiment of the present invention. As shown in fig. 2, in some embodiments, an air quality monitoring method is applied to the electronic device 12 shown in fig. 1, the method comprising:
s210, acquiring air quality data of the to-be-detected points, and constructing tensor data of the to-be-detected points according to the air quality data.
In the embodiment of the invention, the to-be-detected point is the position point of the air quality monitoring station 11. From the air quality data, a 4D tensor data can be constructed
Figure SMS_1
Its respective modulus number is I 1 、I 2 、I 3 、I 4 . The meanings corresponding to the four dimensions are respectively: the longitudinal and lateral extent of the monitoring point in the geographic location, the time series of air contaminant concentrations, and the type of contaminant concentration.
S220, performing Tucker decomposition on the tensor data to obtain a kernel tensor and a factor matrix corresponding to each mode.
In the embodiment of the invention, the tensor data is subjected to Tucker decomposition, so that the nuclear tensor can be obtained
Figure SMS_2
Factor matrix corresponding to each mode>
Figure SMS_3
。
S230, inputting tensor data, a nuclear tensor and factor matrixes corresponding to all modes into a pre-established tensor completion model, and solving the tensor completion model by adopting an optimization minimization method to obtain a reconstruction tensor; the tensor complement model is provided with a kernel norm; the kernel norm is used for representing the low rank property of the factor matrix corresponding to each module; and a log-sum penalty function is also arranged for processing the structural sparsity of the kernel tensor.
In the embodiment of the invention, after the tensor data Tucker is decomposed and reduced in dimension, a group of strong-interaction smaller-scale nuclear tensors (smaller ranks of all modes) and factor matrixes corresponding to all modes are found, and the low rank property of the tensor data is jointly described through the low rank structure of the factor matrixes generated by decomposition and the structural sparsity of the nuclear tensors generated by decomposition, so that a reconstruction tensor capable of reflecting the low rank property can be obtained.
S240, complementing the tensor data of the detection points according to the reconstruction tensor to obtain the complemented tensor data.
S250, determining an air quality monitoring result of the to-be-detected point according to the tensor data after the completion.
In the embodiment of the invention, the reconstruction tensor is constructed through the low-rank structure of the factor matrix and the structural sparsity of the nuclear tensor generated by decomposing the tensor data Tucker, so that the low-rank property among the dimensions of the tensor data is depicted, the tensor data is complemented, and the accurate monitoring of the air quality is realized.
In some embodiments, the tensor complement model is:
Figure SMS_4
(1)
Figure SMS_5
(2)
Figure SMS_6
(3)
wherein ,
Figure SMS_11
for penalty function->
Figure SMS_9
For nuclear tensor>
Figure SMS_18
Representation->
Figure SMS_12
First->
Figure SMS_17
The>
Figure SMS_23
Go (go)/(go)>
Figure SMS_26
Representation->
Figure SMS_14
First->
Figure SMS_22
Sum of squares of all elements of row, +.>
Figure SMS_7
Is the Frobenius norm, +.>
Figure SMS_19
Representing the matrix core norms of the matrix,γfor the first parameter, low rank of the factor matrix for balancing sparsity of the kernel tensor,/->
Figure SMS_8
，/>
Figure SMS_15
Is a factor matrix->
Figure SMS_13
Weight of->
Figure SMS_16
As a second parameter, the first parameter is,vfor approximating parameters +.>
Figure SMS_20
，/>
Figure SMS_24
For the reconstructed 4D tensor, +.>
Figure SMS_21
In order to be a tensor data,
Figure SMS_25
representation->
Figure SMS_10
Is a non-zero term of (2).
In the embodiment of the invention, because of the incompleteness of the air quality data (only including partial monitoring point data), the obtained tensor
Figure SMS_27
There will naturally be some low rank representation. We will tensor data->
Figure SMS_28
Performing Tucker decomposition, and co-characterizing tensors by using low-rank structure of the generated factor matrix and structural sparsity of the nuclear tensors>
Figure SMS_29
Low rank of (c) is provided. In order to achieve the required low rank of the factor matrix (while reflecting the low rank of the kernel tensor), the kernel norm is introduced in the tensor complement optimization model. Due to tensor data->
Figure SMS_30
Self-imperfections, a Tensor Completeness (TC) framework is embedded, i.e., equations (1) - (3) above.
In some embodiments, S230 may include: inputting the tensor data, the kernel tensor generated after the tensor data Tucker decomposition and factor matrixes corresponding to all modes into a pre-established tensor completion model; determining the original constraint of the tensor complement model according to a Tikhonov regularization method; and solving the tensor complement model by adopting an optimization minimization method of the imprecise alternating direction to obtain a reconstruction tensor.
In an embodiment of the present invention, in order to solve the tensor complement model, optimization-Minimization (MM) is used, i.e. a given objective function is optimized by iteratively minimizing a simple proxy function.
Before using the MM method, we first approximated the original constraint problem using the Tikhonov regularization method:
Figure SMS_31
(4)
wherein ,μis a regularization parameter which is used to determine the regularization,
Figure SMS_32
. Obviously, the minimization function +.>
Figure SMS_33
Is a matrix comprising factors->
Figure SMS_34
Nuclear tensor->
Figure SMS_35
And reconstruction tensor->
Figure SMS_36
And is a non-convex function, it is difficult to obtain a display solution for the variable.
In order to solve the problems, a non-precise alternating direction method (Inexact Alternating Direction Method, IADM) can be embedded into the MM algorithm, namely, an optimization problem with a certain non-precise standard is decomposed into small sub-problems which are easy to process, the objective function corresponding to each small sub-problem is monotonous and does not rise, and the solved variables can be displayed.
In some embodiments, the method includes inputting tensor data, a kernel tensor generated after decomposition of the tensor data Tucker, and factor matrices corresponding to each mode into a pre-established tensor complement model, solving the tensor complement model by combining a non-precise alternating direction method and an optimization minimization method to obtain a reconstructed tensor, including: obtaining an updated nuclear tensor according to tensor data, the nuclear tensor, factor matrixes corresponding to all modes and an MFISTA algorithm; updating the factor matrix corresponding to each mode according to a preset updating formula to obtain a plurality of updated factor matrices; obtaining updated tensor data according to the updated kernel tensor and the updated factor matrix corresponding to each mode; judging whether the tensor data meets a preset rule; when the tensor data meets a preset rule, the updated tensor data is used as a reconstruction tensor; and when the tensor data does not meet the preset rule, jumping to obtain an updated nuclear tensor according to the tensor data, the nuclear tensor, the factor matrix corresponding to each mode and the MFISTA algorithm.
In the embodiment of the invention, the input of the IADM-MM algorithm is as follows: initial tensor data X 0 First parameterγFactor matrix
Figure SMS_37
Weight of +.>
Figure SMS_38
Preset timet max The output is tensor data X.
After combining the algorithm of the combination of the imprecise alternating direction method and the optimization minimization method, the updating process of the kernel tensor is as follows:
1. initializing: selection of
Figure SMS_39
，/>
Figure SMS_40
，/>
Figure SMS_41
Setting upt=0。
2. Updating a kernel tensor according to an MFISTA algorithm
Figure SMS_42
。
3. Updating the factor matrix corresponding to each mode according to a preset updating formula
Figure SMS_43
。
4. According to updating
Figure SMS_44
And updated->
Figure SMS_45
Updating tensor data by presetting an updating formula>
Figure SMS_46
。
5. When the tensor data meets the preset rule, a reconstruction tensor is obtained, and when the tensor data does not meet the preset rule, the method comprises the steps oft=t+1, jump to step 2.
The preset rules are as follows: when the iteration number reaches a certain prescribed value
Figure SMS_47
The iterative process will terminate when or when the following conditions are met. The specific decision formula of the preset rule is as follows:
Figure SMS_48
(5)
wherein the parameters are
Figure SMS_49
η is a very small number.
Each pair of tensor data
Figure SMS_50
After one update, before the end of the present iteration, the kernel tensor can be removed according to the rank reduction strategy of the given threshold>
Figure SMS_51
Negligible row and factor matrix for each mode expansion of (2)>
Figure SMS_52
A corresponding column. The method comprises the following steps:
taking in each iteration
Figure SMS_53
After that, according to the nuclear tensor->
Figure SMS_54
Determining a factor matrix +.>
Figure SMS_55
May exist. />
Figure SMS_56
Redundancy line of (1) and its set->
Figure SMS_57
The strict definition is as follows:
Figure SMS_58
(6)
if it is
Figure SMS_59
Then the first can be ignored significantlynModulo corresponding factor matrix->
Figure SMS_60
Is the first of (2)jColumns. However, removing negligible components according to this strict definition is difficult to achieve. Thus, a more relaxed criterion may be used:
Figure SMS_61
(7)
wherein ,
Figure SMS_62
is a nuclear tensor->
Figure SMS_66
First, thenModulo the set of expanded redundant rows, +.>
Figure SMS_68
(e.g.)>
Figure SMS_63
) This means +.>
Figure SMS_65
And->
Figure SMS_67
There is a large gap between them. And simultaneously, the strong interaction between the factor matrix and the nuclear tensor is very naturally shown. Finally, the nuclear tensor->
Figure SMS_69
And factor matrix->
Figure SMS_64
The negligible components of (c) are deleted by:
Figure SMS_70
(8)
wherein ,
Figure SMS_71
is->
Figure SMS_72
Is a complement of the above.
In some embodiments, obtaining the updated kernel tensor according to the tensor data, the kernel tensor, the factor matrix corresponding to each mode and the MFISTA algorithm includes: calculating a first optimized tensor according to the kernel tensor; calculating characteristic parameters according to factor matrixes corresponding to the modes; according to the characteristic parameters, a positive scalar is obtained; and performing iterative optimization for the nuclear tensor for preset times according to the tensor data, the factor matrix corresponding to each mode, the first optimized tensor and the positive scalar, and obtaining the updated nuclear tensor.
In an embodiment of the invention, in order to obtain a kernel tensor
Figure SMS_73
In a closed form, we first introduce
Figure SMS_74
Is a proxy function of (a):
Figure SMS_75
(9)
obviously, when
Figure SMS_76
=/>
Figure SMS_77
When the inequality (9) equation is established.
Figure SMS_78
(10)
Wherein the first optimized tensor
Figure SMS_79
Is one and->
Figure SMS_80
Tensors of the same size, the +.>
Figure SMS_81
The elements are as follows:
Figure SMS_82
(11)
thus, it is possible to obtain:
Figure SMS_83
(12)
wherein ,
Figure SMS_84
. Obviously->
Figure SMS_85
Is->
Figure SMS_86
Is a proxy function of (1), and->
Figure SMS_87
At the same time, it is also possible to obtain:
Figure SMS_88
(13)
thus, by solving (4) the transformation into iteratively minimized proxy function (12), one can get by solving the following optimization problem
Figure SMS_89
Is updated by:
Figure SMS_90
(14)
order the
Figure SMS_91
，/>
Figure SMS_92
，/>
Figure SMS_93
，/>
Figure SMS_94
. The optimization of equation (14) can be expressed as:
Figure SMS_95
(15)
thus, the above formula may yield the following unique solution:
Figure SMS_96
(16)
as can be seen from the above equation, it is directly derived from equation (16)
Figure SMS_97
Is expensive because of the matrix->
Figure SMS_98
The inverse computational complexity of (2) is +.>
Figure SMS_99
。
To speed up the computation, we use an iterative algorithm called the over-relaxed monotonic fast iterative shrinkage threshold algorithm (Monotone Fast Iterative Shrinkage-thresholding Algorithm, MFISTA). The algorithm is generally used to solve many large-scale optimization problems and for the minimization of the sum of a smooth function and a possibly non-smooth convex function, not only guarantees a monotonic decrease of the objective function, but also allows a variable step size over a larger range (calculation of step size can be done by the following formula
Figure SMS_100
Obtained by->
Figure SMS_101
) While ensuring convergence speed as
Figure SMS_102
, wherein kIs the number of iterations. Equation (15) is a convex function and can thereforeTo effectively solve (15) using the over-relaxed MFISTA.
Equation (15) can be expressed as:
Figure SMS_103
. Direct calculation
Figure SMS_104
Or a more efficient tensor solution:
Figure SMS_105
(17)
furthermore, for any given positive scalar
Figure SMS_106
Neighbor operator->
Figure SMS_107
Has the following closed form:
Figure SMS_108
(18)
wherein ,
Figure SMS_109
is in combination with->
Figure SMS_110
Identity matrix of the same size, due to +.>
Figure SMS_111
Is a diagonal matrix, matrix->
Figure SMS_112
The inverse of (2) can be readily obtained. Note that (I) is->
Figure SMS_113
Is Lipschitz continuous and has a Lipschitz constant:
Figure SMS_114
(19)
wherein ,
Figure SMS_115
representing the maximum eigenvalue of matrix Y.
Wherein the input of the MFISTA algorithm is a kernel tensor
Figure SMS_116
Tensor data->
Figure SMS_117
Factor matrix->
Figure SMS_118
、/>
Figure SMS_119
And maximum number of iterationsk max Output is +.>
Figure SMS_120
The MFISTA algorithm comprises the following specific steps:
2.1 calculating a first optimized tensor by equation (11) and equation (19)
Figure SMS_121
And characteristic parameter->
Figure SMS_122
。
2.2 from
Figure SMS_123
Is selected to be positive scalar +.>
Figure SMS_124
。
2.3, orderk=1, the following process is cycled untilk=k max 。
Calculation according to (17)
Figure SMS_125
；
Order the
Figure SMS_126
、/>
Figure SMS_127
、
Figure SMS_128
、/>
Figure SMS_129
。
2.4，
Figure SMS_130
。
In some embodiments, the preset update formula is:
Figure SMS_131
(20)
wherein ,
Figure SMS_134
to the updated firstnModulo corresponding factor matrix,/>
Figure SMS_136
Is the firstnThe matrix of factors to which the mode corresponds,
Figure SMS_139
，/>
Figure SMS_133
，/>
Figure SMS_137
，
Figure SMS_140
，/>
Figure SMS_141
if the singular value decomposition for an arbitrary matrix Z is +.>
Figure SMS_132
Then->
Figure SMS_135
，/>
Figure SMS_138
。
In the embodiment of the invention, for
Figure SMS_142
Optionally give->
Figure SMS_143
Factor matrix->
Figure SMS_144
The update of (2) may be obtained by:
Figure SMS_145
(21)
wherein ,
Figure SMS_146
is a closed convex but not microscopic function, and
Figure SMS_147
，/>
Figure SMS_148
is a convex quadratic function. To get->
Figure SMS_149
Is a closed approximation of->
Figure SMS_150
Based on it is currently->
Figure SMS_151
The above equation (20) can be obtained by the optimization technique of the first-order taylor expansion.
In some embodiments, the updated tensor data is calculated as:
Figure SMS_152
(22)
wherein ,
Figure SMS_154
for the updated kernel tensor +.>
Figure SMS_156
To the updated firstnModulo corresponding factor matrix,/>
Figure SMS_158
For the reconstructed 4D tensor, +.>
Figure SMS_155
For tensor data, +.>
Figure SMS_157
Representation->
Figure SMS_159
Non-zero term of->
Figure SMS_160
Representation->
Figure SMS_153
Is a non-zero term of (2).
In the embodiment of the invention, in order to distinguish the physical quantity before and after updating, the nuclear tensor obtained by final updating can be obtained
Figure SMS_161
Marked as->
Figure SMS_162
The factor matrix corresponding to each mode obtained by final updating is +.>
Figure SMS_163
Marked as->
Figure SMS_164
。
Fig. 4 is a flowchart of an implementation of an air quality monitoring method according to another embodiment of the present invention. As shown in fig. 4, in some embodiments, after determining the air quality monitoring result of the point to be detected, the method further comprises: evaluating an air quality monitoring result according to a preset evaluation formula; wherein the preset evaluation formula comprises at least one of the following: root mean square error formula, average absolute percentage error formula.
In the embodiment of the invention, the root mean square error formula is:
Figure SMS_165
(23)
the average absolute error formula is:
Figure SMS_166
(24)
the average absolute percentage error formula is:
Figure SMS_167
(25)
wherein ,
Figure SMS_168
for predictive value +.>
Figure SMS_169
Is true value +.>
Figure SMS_170
For the number of missing data, +.>
Figure SMS_171
The function is represented for vectorization.
As shown in fig. 4, after the evaluation is completed, if the evaluation result meets the requirements, the monitoring result is valid, if the evaluation result does not meet the requirements, the monitoring result is invalid, parameters in the tensor completion model are adjusted, the reconstruction tensor is recalculated and completed again, until the evaluation result meets the requirements.
In summary, the beneficial effects of the invention are as follows:
the reconstruction tensor is constructed through the low-rank structure of the factor matrix generated by decomposition and the structural sparsity of the nuclear tensor, so that the low-rank property among the dimensions of the tensor data is described, the tensor data is complemented, and the accurate monitoring of the air quality is realized.
It should be understood that the sequence number of each step in the foregoing embodiment does not mean that the execution sequence of each process should be determined by the function and the internal logic, and should not limit the implementation process of the embodiment of the present invention.
Fig. 4 is a schematic structural diagram of an air quality monitoring device according to an embodiment of the present invention. As shown in fig. 4, in some embodiments, the air quality monitoring device 4 comprises:
the acquiring module 410 is configured to acquire air quality data of a to-be-detected point, and construct tensor data of the to-be-detected point according to the air quality data;
the decomposition module 420 is configured to perform a Tucker decomposition on the tensor data to obtain a kernel tensor and a factor matrix corresponding to each mode;
the reconstruction module 430 is configured to input the kernel tensor, the factor matrix corresponding to each module, and tensor data into a pre-established tensor complement model, and solve the tensor complement model by adopting an optimization minimization method to obtain a reconstructed tensor; the tensor complement model is provided with a kernel norm; the kernel norm is used for representing the low rank property of the factor matrix corresponding to each module; the log-sum penalty function is used to handle the structural sparsity of the kernel tensor;
the complementing module 440 is configured to complement the tensor data of the detection point according to the reconstructed tensor, so as to obtain the tensor data after being complemented;
the determining module 450 is configured to determine an air quality monitoring result of the to-be-detected point according to the completed tensor data.
Optionally, the reconstruction module 430 is specifically configured to: inputting tensor data, a nuclear tensor and factor matrixes corresponding to all modes into a pre-established tensor complement model; determining the original constraint of the tensor complement model according to a Tikhonov regularization method; and solving the tensor complement model by combining a non-precise alternating direction method and an optimization minimization method to obtain a reconstruction tensor.
Optionally, the tensor complement model is:
Figure SMS_172
Figure SMS_173
wherein ,
Figure SMS_177
for penalty function->
Figure SMS_178
For nuclear tensor>
Figure SMS_183
Representation->
Figure SMS_175
First->
Figure SMS_182
The>
Figure SMS_176
Go (go)/(go)>
Figure SMS_186
Representation->
Figure SMS_187
First->
Figure SMS_192
Sum of squares of all elements of row, +.>
Figure SMS_179
Is the Frobenius norm, +.>
Figure SMS_189
Representing the matrix core norms of the matrix,γfor the first parameter, low rank of the factor matrix for balancing sparsity of the kernel tensor,/->
Figure SMS_181
，/>
Figure SMS_188
Is a factor matrix->
Figure SMS_190
Weight of->
Figure SMS_193
As a second parameter, the first parameter is,vfor approximating parameters +.>
Figure SMS_174
，/>
Figure SMS_184
For the reconstructed 4D tensor, +.>
Figure SMS_185
In order to be a tensor data,
Figure SMS_191
representation->
Figure SMS_180
Is a non-zero term of (2).
Optionally, the reconstruction module 430 is specifically configured to: obtaining an updated nuclear tensor according to tensor data, the nuclear tensor, factor matrixes corresponding to all modes and an MFISTA algorithm; updating the factor matrix corresponding to each mode according to a preset updating formula to obtain a plurality of updated factor matrices; obtaining updated tensor data according to the updated kernel tensor and the updated factor matrix corresponding to each mode; judging whether the tensor data meets a preset rule; when the tensor data meets a preset rule, the updated tensor data is used as a reconstruction tensor; and when the tensor data does not meet the preset rule, jumping to obtain an updated nuclear tensor according to the tensor data, the nuclear tensor, the factor matrix corresponding to each mode and the MFISTA algorithm.
Optionally, the reconstruction module 430 is specifically configured to: calculating a first optimized tensor according to the kernel tensor; calculating characteristic parameters according to factor matrixes corresponding to the modes; selecting a positive scalar according to the characteristic parameters; and performing iterative optimization for the nuclear tensor for preset times according to the tensor data, the factor matrix corresponding to each mode, the first optimized tensor and the positive scalar, and obtaining the updated nuclear tensor.
Optionally, the preset update formula is:
Figure SMS_194
wherein ,
Figure SMS_197
to the updated firstnModulo corresponding factor matrix,/>
Figure SMS_199
Is the firstnThe matrix of factors to which the mode corresponds,
Figure SMS_202
，/>
Figure SMS_196
，/>
Figure SMS_200
，
Figure SMS_203
，/>
Figure SMS_204
if the singular value decomposition for an arbitrary matrix Z is +.>
Figure SMS_195
Then->
Figure SMS_198
，/>
Figure SMS_201
。/>
Optionally, the calculation formula of the updated tensor data is:
Figure SMS_205
wherein ,
Figure SMS_206
for the updated kernel tensor +.>
Figure SMS_209
To the updated firstnModulo corresponding factor matrix,/>
Figure SMS_211
For the reconstructed 4D tensor, +.>
Figure SMS_208
For tensor data, +.>
Figure SMS_210
Representation->
Figure SMS_212
Non-zero term of->
Figure SMS_213
Representation->
Figure SMS_207
Is a non-zero term of (2).
Optionally, the air quality monitoring device 4 further includes: the evaluation module is used for evaluating the air quality monitoring result according to a preset evaluation formula; wherein the preset evaluation formula comprises at least one of the following: root mean square error formula, average absolute percentage error formula.
The air quality monitoring device provided in this embodiment may be used to execute the above method embodiment, and its implementation principle and technical effects are similar, and this embodiment will not be described here again.
Fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the present invention. As shown in fig. 5, an electronic device 5 according to an embodiment of the present invention is provided, the electronic device 5 of the embodiment including: a processor 50, a memory 51 and a computer program 52 stored in the memory 51 and executable on the processor 50. The steps of the various air quality monitoring method embodiments described above, such as steps 210 through 250 shown in fig. 2, are implemented by the processor 50 when executing the computer program 52. Alternatively, the processor 50, when executing the computer program 52, performs the functions of the modules/units of the system embodiments described above, such as the functions of the modules 410-450 shown in fig. 4.
By way of example, the computer program 52 may be partitioned into one or more modules/units, which are stored in the memory 51 and executed by the processor 50 to complete the present invention. One or more of the modules/units may be a series of computer program instruction segments capable of performing a specific function for describing the execution of the computer program 52 in the electronic device 5.
The electronic device 5 may be a terminal, a server, or the like, and is not limited thereto, and the server may be a physical server, a cloud server, or the like. The electronic device 5 may include, but is not limited to, a processor 50, a memory 51. It will be appreciated by those skilled in the art that fig. 5 is merely an example of the electronic device 5 and is not meant to be limiting as the electronic device 5, may include more or fewer components than shown, or may combine certain components, or different components, e.g., the electronic device may further include an input-output device, a network access device, a bus, etc.
The processor 50 may be a central processing unit (Central Processing Unit, CPU), other general purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), field-programmable gate arrays (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory 51 may be an internal storage unit of the electronic device 5, such as a hard disk or a memory of the electronic device 5. The memory 51 may also be an external storage device of the electronic device 5, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card) or the like, which are provided on the electronic device 5. Further, the memory 51 may also include both an internal storage unit and an external storage device of the electronic device 5. The memory 51 is used to store computer programs and other programs and data required by the electronic device. The memory 51 may also be used to temporarily store data that has been output or is to be output.
An embodiment of the present invention provides a computer readable storage medium storing a computer program which, when executed by a processor, implements the steps of the above-described air quality monitoring method embodiment.
The computer readable storage medium stores a computer program 52, the computer program 52 includes program instructions, which when executed by the processor 50 implement all or part of the procedures of the method embodiments described above, or may be implemented by means of hardware associated with the instructions of the computer program 52, the computer program 52 may be stored in a computer readable storage medium, and the computer program 52, when executed by the processor 50, implements the steps of the method embodiments described above. The computer program 52 comprises computer program code, which may be in the form of source code, object code, executable files, or in some intermediate form, among others. The computer readable medium may include: any entity or device capable of carrying computer program code, a recording medium, a U disk, a removable hard disk, a magnetic disk, an optical disk, a computer Memory, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), an electrical carrier signal, a telecommunications signal, a software distribution medium, and so forth.
The computer readable storage medium may be an internal storage unit of the electronic device of any of the foregoing embodiments, such as a hard disk or a memory of the electronic device. The computer readable storage medium may also be an external storage device of the electronic device, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card) or the like, which are provided on the electronic device. Further, the computer-readable storage medium may also include both internal storage units and external storage devices of the electronic device. The computer-readable storage medium is used to store a computer program and other programs and data required for the electronic device. The computer-readable storage medium may also be used to temporarily store data that has been output or is to be output.
It should be understood that the sequence number of each step in the foregoing embodiment does not mean that the execution sequence of each process should be determined by the function and the internal logic, and should not limit the implementation process of the embodiment of the present invention.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-described division of the functional units and modules is illustrated, and in practical application, the above-described functional distribution may be performed by different functional units and modules according to needs, i.e. the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-described functions. The functional units and modules in the embodiment may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit, where the integrated units may be implemented in a form of hardware or a form of a software functional unit. In addition, specific names of the functional units and modules are only for convenience of distinguishing from each other, and are not used for limiting the protection scope of the present application. The specific working process of the units and modules in the above system may refer to the corresponding process in the foregoing method embodiment, which is not described herein again.
In the foregoing embodiments, the descriptions of the embodiments are emphasized, and in part, not described or illustrated in any particular embodiment, reference is made to the related descriptions of other embodiments.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
In the embodiments provided in the present invention, it should be understood that the disclosed apparatus/electronic device and method may be implemented in other manners. For example, the apparatus/electronic device embodiments described above are merely illustrative, e.g., the division of modules or units is merely a logical functional division, and there may be additional divisions when actually implemented, e.g., multiple units or components may be combined or integrated into another system, or some features may be omitted, or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection via interfaces, devices or units, which may be in electrical, mechanical or other forms.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed over a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
In addition, each functional unit in the embodiments of the present invention may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit. The integrated units may be implemented in hardware or in software functional units.
The integrated modules/units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the present invention may implement all or part of the flow of the method of the above embodiment, or may be implemented by a computer program to instruct related hardware, and the computer program may be stored in a computer readable storage medium, where the computer program, when executed by a processor, may implement the steps of each of the method embodiments described above. Wherein the computer program comprises computer program code, which may be in the form of source code, object code, executable files or in some intermediate form, etc. The computer readable medium may include: any entity or device capable of carrying computer program code, a recording medium, a U disk, a removable hard disk, a magnetic disk, an optical disk, a computer Memory, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), an electrical carrier signal, a telecommunications signal, a software distribution medium, and so forth.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention, and are intended to be included in the scope of the present invention.

Claims (9)

1. An air quality monitoring method, comprising:
acquiring air quality data of a to-be-detected point, and constructing tensor data of the to-be-detected point according to the air quality data;
performing Tucker decomposition on the tensor data to obtain a kernel tensor and a factor matrix corresponding to each mode;
inputting the nuclear tensor, the factor matrix corresponding to each mode and the tensor data into a pre-established tensor complement model, and solving the tensor complement model by adopting an optimization minimization method to obtain a reconstruction tensor; the tensor completion model is provided with a kernel norm and a log-sum penalty function; the kernel norm is used for representing the low rank property of the factor matrix corresponding to each module, and the log-sum penalty function is used for processing the structural sparsity of the kernel tensor;
completing tensor data of the to-be-detected points according to the reconstruction tensor to obtain completed tensor data;
determining an air quality monitoring result of the to-be-detected point according to the tensor data after the completion;
the tensor complement model is:
Figure QLYQS_1
Figure QLYQS_2
wherein ,
Figure QLYQS_20
for penalty function->
Figure QLYQS_8
For the nuclear tensor +_>
Figure QLYQS_17
Representation->
Figure QLYQS_7
First->
Figure QLYQS_16
The>
Figure QLYQS_19
Go (go)/(go)>
Figure QLYQS_22
Representation->
Figure QLYQS_6
First->
Figure QLYQS_12
Sum of squares of all elements of row, +.>
Figure QLYQS_3
Is the Frobenius norm, +.>
Figure QLYQS_15
Representing the matrix core norms of the matrix,γfor the first parameter, low rank of the factor matrix for balancing sparsity of the kernel tensor,/->
Figure QLYQS_10
，/>
Figure QLYQS_18
Is a factor matrix->
Figure QLYQS_9
Weight of->
Figure QLYQS_13
As a second parameter, the first parameter is,vfor approximating parameters +.>
Figure QLYQS_4
，/>
Figure QLYQS_11
For the reconstructed 4D tensor, +.>
Figure QLYQS_14
For the tensor data, < > for>
Figure QLYQS_21
Representation->
Figure QLYQS_5
Is a non-zero term of (2).
2. The air quality monitoring method according to claim 1, wherein inputting the nuclear tensor, the factor matrix corresponding to each mode, and the tensor data into a pre-established tensor complement model, and solving the tensor complement model by adopting an optimization minimization method to obtain a reconstructed tensor comprises:
inputting the tensor data, the nuclear tensor and the factor matrix corresponding to each mode into a pre-established tensor complement model;
according to a Tikhonov regularization method, determining an original constraint of the tensor complement model;
and solving the tensor complement model by adopting an optimization minimization method of the imprecise alternating direction to obtain the reconstruction tensor.
3. The air quality monitoring method according to claim 2, wherein the nuclear tensor, the factor matrix corresponding to each mode, and the tensor data are input into a pre-established tensor complement model, and the tensor complement model is solved by adopting an optimization minimization method of an imprecise alternating direction, so as to obtain the reconstruction tensor, including:
obtaining an updated nuclear tensor according to the tensor data, the nuclear tensor, the factor matrix corresponding to each mode and an MFISTA algorithm;
updating the factor matrix corresponding to each mode according to a preset updating formula to obtain a plurality of updated factor matrices;
obtaining updated tensor data according to the updated kernel tensor and the updated factor matrix corresponding to each mode;
judging whether the updated tensor data meets a preset rule or not;
when the updated tensor data meets a preset rule, the updated tensor data is used as the reconstruction tensor;
and when the updated tensor data does not meet the preset rule, jumping to obtain the updated tensor according to the tensor data, the tensor, the factor matrix corresponding to each mode and the MFISTA algorithm.
4. The air quality monitoring method according to claim 3, wherein the obtaining the updated kernel tensor according to the tensor data, the kernel tensor, the factor matrix corresponding to each mode, and an MFISTA algorithm includes:
calculating a first optimized tensor according to the kernel tensor;
calculating characteristic parameters according to the factor matrixes corresponding to the modes;
selecting a positive scalar according to the characteristic parameters;
and carrying out iterative optimization for the nuclear tensor for preset times according to the tensor data, the factor matrix corresponding to each mode, the first optimized tensor and the positive scalar to obtain an updated nuclear tensor.
5. The air quality monitoring method according to claim 3, wherein the update formula of the factor matrix corresponding to each mode is preset as follows:
Figure QLYQS_23
wherein ,
Figure QLYQS_25
to the updated firstnModulo factor matrix (M;)>
Figure QLYQS_29
Is the firstnFactor matrix of the module, ">
Figure QLYQS_32
，
Figure QLYQS_26
，/>
Figure QLYQS_27
，/>
Figure QLYQS_30
，
Figure QLYQS_33
If for any matrixＺSingular value decomposition into +.>
Figure QLYQS_24
Then
Figure QLYQS_28
，/>
Figure QLYQS_31
，μ>0，μIs a regularization parameter.
6. The air quality monitoring method according to claim 3, wherein the updated tensor data is calculated as:
Figure QLYQS_34
wherein ,
Figure QLYQS_35
for the updated kernel tensor +.>
Figure QLYQS_39
To the updated firstnFactor matrix of the module, ">
Figure QLYQS_41
For the reconstructed 4D tensor, +.>
Figure QLYQS_37
For the tensor data, < > for>
Figure QLYQS_38
Representation->
Figure QLYQS_40
Non-zero term of->
Figure QLYQS_42
Representation->
Figure QLYQS_36
Is a non-zero term of (2).
7. The air quality monitoring method according to any one of claims 1 to 6, wherein after determining the air quality monitoring result of the point to be detected, the method further comprises:
evaluating the air quality monitoring result according to a preset evaluation formula; wherein the preset evaluation formula comprises at least one of the following: root mean square error formula, average absolute percentage error formula.
8. An electronic device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the air quality monitoring method according to any of the preceding claims 1 to 7 when the computer program is executed.
9. A computer readable storage medium, characterized in that it stores a computer program which, when executed by a processor, implements the steps of the air quality monitoring method according to any of the preceding claims 1 to 7.
CN202310347881.3A 2023-04-04 2023-04-04 Air quality monitoring method, electronic equipment and storage medium Active CN116087435B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202310347881.3A CN116087435B (en) 2023-04-04 2023-04-04 Air quality monitoring method, electronic equipment and storage medium

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202310347881.3A CN116087435B (en) 2023-04-04 2023-04-04 Air quality monitoring method, electronic equipment and storage medium

Publications (2)

Publication Number Publication Date
CN116087435A CN116087435A (en) 2023-05-09
CN116087435B true CN116087435B (en) 2023-06-16

Family

ID=86187173

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202310347881.3A Active CN116087435B (en) 2023-04-04 2023-04-04 Air quality monitoring method, electronic equipment and storage medium

Country Status (1)

Country Link
CN (1) CN116087435B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116451058A (en) * 2023-06-20 2023-07-18 石家庄学院 Tensor completion-based multi-source heterogeneous data feature extraction method, device and medium

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112836368A (en) * 2021-01-29 2021-05-25 南开大学 Greenhouse parameter model construction and recovery method based on low-rank tensor
CN114841888A (en) * 2022-05-16 2022-08-02 电子科技大学 Visual data completion method based on low-rank tensor ring decomposition and factor prior
KR20220145007A (en) * 2021-04-21 2022-10-28 삼성전자주식회사 Data Processing Method of Detecting and Recovering Missing Values, Outliers and Patterns in Tensor Stream Data

Family Cites Families (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8458109B2 (en) * 2009-05-27 2013-06-04 Yin Zhang Method and apparatus for spatio-temporal compressive sensing
CN110568486B (en) * 2019-09-17 2020-06-30 电子科技大学 Seismic signal completion method based on synchronous sparse low-rank tensor completion model
CN112990264A (en) * 2021-02-08 2021-06-18 浙江师范大学 Multi-view clustering method based on consistent graph learning
CN113935190A (en) * 2021-11-02 2022-01-14 重庆邮电大学 Tensor expression-based air pollutant concentration accurate monitoring method and system
CN115130770A (en) * 2022-02-21 2022-09-30 攀枝花学院 Tensor feature reconstruction-based industrial wastewater discharge water quality prediction method

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112836368A (en) * 2021-01-29 2021-05-25 南开大学 Greenhouse parameter model construction and recovery method based on low-rank tensor
KR20220145007A (en) * 2021-04-21 2022-10-28 삼성전자주식회사 Data Processing Method of Detecting and Recovering Missing Values, Outliers and Patterns in Tensor Stream Data
CN114841888A (en) * 2022-05-16 2022-08-02 电子科技大学 Visual data completion method based on low-rank tensor ring decomposition and factor prior

Also Published As

Publication number Publication date
CN116087435A (en) 2023-05-09

Similar Documents

Publication Publication Date Title
Sangiorgio et al. Robustness of LSTM neural networks for multi-step forecasting of chaotic time series
Scrucca GA: A package for genetic algorithms in R
CN110909926A (en) TCN-LSTM-based solar photovoltaic power generation prediction method
CN116087435B (en) Air quality monitoring method, electronic equipment and storage medium
Ascia et al. Performance evaluation of efficient multi-objective evolutionary algorithms for design space exploration of embedded computer systems
CN116186522B (en) Big data core feature extraction method, electronic equipment and storage medium
Shabri et al. Crude oil price forecasting based on hybridizing wavelet multiple linear regression model, particle swarm optimization techniques, and principal component analysis
CN106651464A (en) Agricultural product price prediction method and apparatus
Qian et al. A probabilistic approach to neural network pruning
CN115660233A (en) Photovoltaic power prediction method and device, electronic equipment and storage medium
CN112560966A (en) Polarimetric SAR image classification method, medium and equipment based on scattergram convolution network
Li et al. PENNI: Pruned kernel sharing for efficient CNN inference
CN106599610A (en) Method and system for predicting association between long non-coding RNA and protein
CN116346639A (en) Network traffic prediction method, system, medium, equipment and terminal
Seo et al. Graph neural networks and implicit neural representation for near-optimal topology prediction over irregular design domains
Xu et al. Dynamic graph neural network with adaptive edge attributes for air quality prediction: A case study in China
CN111478742B (en) SM4 algorithm analysis method, system and equipment
CN116384244A (en) Electromagnetic field prediction method based on physical enhancement neural network
CN111859785B (en) Fluid feature extraction method, system, computer-readable storage medium and device
KR102507014B1 (en) Method and apparatus for energy-aware deep neural network compression
US20240103920A1 (en) Method and system for accelerating the convergence of an iterative computation code of physical parameters of a multi-parameter system
CN111523647B (en) Network model training method and device, feature selection model, method and device
Li et al. Multi-variable regression methods using modified Chebyshev polynomials of class 2
CN113779861A (en) Photovoltaic power prediction method and terminal equipment
Zhang et al. Hardware-aware one-shot neural architecture search in coordinate ascent framework

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
TR01 Transfer of patent right

Effective date of registration: 20230801

Address after: 050051 Floor 5, No. 2, Xiangyi Road, Xinhua District, Shijiazhuang City, Hebei Province

Patentee after: Hebei Linghe Computer Information Technology Co.,Ltd.

Address before: 050035 Shijiazhuang University, No. 288, Zhufeng street, high tech Zone, Shijiazhuang City, Hebei Province

Patentee before: SHIJIAZHUANG University

TR01 Transfer of patent right