Real-time reconstruction method of multi-parameter data of Internet of Things based on subspace

Abstract

The present invention is a subspace-based real-time reconstruction method for multi-parameter data of the Internet of Things. The method first utilizes the spatiotemporal correlation of IoT data and only collects part of the data for transmission, that is, only part of the sampled data is transmitted to the base station in each time slot, so as to reduce the energy consumption required for sensor nodes to collect and transmit data. Secondly, the multi-parameter data collected at continuous moments are organized into tensor forms, making full use of the spatiotemporal correlation between multi-parameter data and the inherent relationship between various types of data; to achieve real-time data reconstruction, the sliding window model is used to introduce historical data; based on Tucker decomposition, the spatial distribution subspace of the current time slot data is obtained from the historical data, and the spatiotemporal correlation and internal connection between the data are fully explored; the current time slot data is reconstructed in real time using the partial sampled data received in the current time slot and the constrained total variation in the spatiotemporal direction.

Description

Technical Field

[0001] The present invention belongs to the technical field of Internet of Things, and specifically is a subspace-based real-time reconstruction method for multi-parameter data of Internet of Things. Background Art

[0002] The Internet of Things (IoT) is the third wave of the development of the information industry since the emergence of computers and the Internet. Its applications have spread to many fields. The IoT device layer consists of a large number of sensor nodes that are capable of sensing and communicating. These nodes can monitor multiple aspects of information in real time. For example, in environmental information monitoring, IoT nodes with multiple types of sensors can simultaneously sense multi-attribute data such as temperature, humidity, light, and voltage. However, multi-attribute data will further increase the transmission volume, resulting in higher network energy consumption. In many application settings, the available network energy is limited, so sparse sensing is usually used to reduce the amount of data transmission, thereby reducing network energy consumption. In sparse sensing data aggregation, how to achieve real-time data transmission when some nodes are in sleep mode is a research difficulty. In addition, since sparse sampling can lead to data loss, reconstruction of multi-parameter data has become an indispensable and important operation in IoT.

[0003] At present, the data reconstruction methods in IoT can be divided into two categories, namely, reconstruction for single-parameter data and multi-parameter data. With the diversification of applications and social production and life needs, IoT nodes with various types of sensors need to collect multi-parameter data at the same time. Therefore, in most cases, multi-parameter data is reconstructed, and the single-parameter data reconstruction method cannot make good use of the internal correlation between multi-parameter data. The existing multi-parameter data reconstruction method is to reconstruct the data after the multi-parameter data of all sampling time slots are converged to the base station, which cannot meet the needs of real-time data reconstruction. Therefore, the present invention proposes a real-time reconstruction method for multi-parameter data of the Internet of Things based on subspace. Summary of the invention

[0004] In view of the shortcomings of the prior art, the technical problem that the present invention intends to solve is to propose a subspace-based real-time reconstruction method for multi-parameter data of the Internet of Things.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] A subspace-based real-time reconstruction method for multi-parameter data of the Internet of Things, characterized in that the method comprises the following steps:

[0007] Step 1: In each time slot, sensor nodes are randomly selected for sampling according to the sampling ratio, and the sampled data is transmitted to the base station. The base station receives part of the sampled data. is the field of real numbers, is the actual number of samples, represents the floor symbol, n is the number of sensor nodes, m is the total number of data types, ρ is the sampling ratio and 0<ρ<<1;

[0008] Step 2: Use the sliding window model to introduce historical data into the current window. The current window data tensor is w is the sliding window width; the current window data tensor Contains historical data and the current time slot data M c Two parts;

[0009] Step 3: Based on Tucker decomposition, the spatial subspace of the current time slot data is obtained from the historical data, and the reconstruction of the current time slot data is converted into the solution formula (4);

[0010] Based on Tucker decomposition, the current window data tensor This breaks down into:

[0011]

[0012] Among them, the factor matrix G (1) , G (2) and G (3) is the spatial distribution subspace, multi-parameter distribution subspace and time distribution subspace of the current window tensor data; G (1) That is, the spatial subspace of the current time slot data; the core tensor represents the interaction level of each subspace;

[0013] The 1-mode matrix of formula (2) is:

[0014]

[0015] Among them, C (1) Represents the core tensor The 1-mode matrix of represents the Kronecker product;

[0016] According to the sliding window model, the 1-mode matrixed data of the current window data tensor can be expressed as [HM c ], H is the historical data 1-mode matrixization of ;

[0017] make G (1) =G,C (1) =C; Based on matrix decomposition, the matrix Φ is decomposed into Φ h , Φ c , then [HM c ]=GC[Φ h Φc ], where H = GCΦ h , M c =GCΦ c ; Let S = GC, so the matrix H is decomposed to get the matrix S. The base station reconstructs the current time slot data in real time through the received partial sampling data d and the constrained total variation in the time and space directions, that is, solves the following equation:

[0018]

[0019] in, represents the reconstructed data matrix, |||| 1 、|||| 2 denote the 1-norm and 2-norm respectively, λ and μ are regularization parameters, Represents the current window data tensor The current time slot data and the previous time slot data in ▽ v The operation is defined as: v (SΦ c )=(SΦ c ) j+1,k -(SΦ c ) j,k , represents the matrix SΦ c The difference between the element in the j+1th row and the kth column and the element in the jth row and the kth column; ▽ l The operation is defined as: l [H c-1 ; SΦ c ]=SΦ c -H c-1 , represents the difference between the corresponding position elements of the current time slot data and the previous time slot data;

[0020] Step 4: Convert the solution of equation (4) into the solution of the following constraint equation:

[0021]

[0022] The augmented Lagrangian function of formula (5) is:

[0023]

[0024] In formula (6), A and B are Lagrange multipliers, α and β are penalty coefficients;

[0025] Step 5: Use the alternating direction multiplication method to solve equation (6) and obtain the matrix Φ c , through M c =SΦ c Reconstruct current time slot data;

[0026] Step 6. Replace the data at the corresponding position in the current time slot data reconstructed in step 5 with the received partial sampling data d according to the index position to obtain the replaced current time slot data. Use the replaced current time slot data as the historical data for reconstructing the next time slot data, and then repeat steps 3 to 6 to realize real-time reconstruction of multi-parameter data.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] First, by utilizing the spatiotemporal correlation of IoT data, only part of the data is collected for transmission, that is, only part of the sampled data is transmitted to the base station in each time slot to reduce the energy consumption required for sensor nodes to collect and transmit data.

[0029] Second, this method organizes the multi-parameter data collected at continuous moments into a tensor form, making full use of the spatiotemporal correlation between multi-parameter data and the intrinsic relationship between various types of data; in order to achieve real-time data reconstruction, the sliding window model is used to introduce historical data; based on Tucker decomposition, the spatial distribution subspace of the current time slot data is obtained from the historical data, and the spatiotemporal correlation and intrinsic connection between the data are fully explored; the current time slot data is reconstructed in real time using the partial sampling data received in the current time slot and the constrained total variation in the spatiotemporal direction. The method of the present invention reconstructs the current time slot data once the sampling data is transmitted to the base station, instead of the existing method of gathering the multi-parameter data of all sampling time slots to the base station and then reconstructing the data. Therefore, the reconstruction of the method of the present invention is more real-time. The comparison results show that the reconstruction error of the method of the present invention is smaller and it is also applicable under different sampling ratios. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 Schematic diagram of data tensor received by the base station in continuous time slots;

[0031] Figure 2 This is the schematic diagram of the sliding window model;

[0032] FIG3( a ) is a diagram showing the error results of temperature reconstruction obtained by the method of the present invention and the prior art method when the sampling ratio is 0.1;

[0033] FIG3( b ) is a diagram showing the error results of humidity reconstruction obtained by the method of the present invention and the prior art method when the sampling ratio is 0.1;

[0034] FIG3(c) is a graph showing the error results of the voltage reconstruction obtained by the method of the present invention and the prior art method when the sampling ratio is 0.1;

[0035] FIG4( a ) is a diagram showing the error results of reconstructing temperature when the sampling ratio is 0.2 using the method of the present invention and the prior art method;

[0036] FIG4( b ) is a diagram showing the error results of humidity reconstruction obtained by the method of the present invention and the prior art method when the sampling ratio is 0.2;

[0037] FIG4(c) is a graph showing the error results of the voltage reconstruction obtained by the method of the present invention and the prior art method when the sampling ratio is 0.2;

[0038] FIG5(a) is a diagram showing the error results of reconstructing temperature when the sampling ratio is 0.3 for the method of the present invention and the prior art method;

[0039] FIG5( b ) is a diagram showing the error results of humidity reconstruction obtained by the method of the present invention and the prior art method when the sampling ratio is 0.3;

[0040] FIG5(c) is a graph showing the error results of the voltage reconstruction obtained by the method of the present invention and the prior art method when the sampling ratio is 0.3. DETAILED DESCRIPTION

[0041] The technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments, but the protection scope of the present application is not limited thereto.

[0042] The present invention provides a subspace-based real-time reconstruction method for multi-parameter data of the Internet of Things (hereinafter referred to as the method), which comprises the following steps:

[0043] Step 1: Assume that the IoT device layer contains n sensor nodes for collecting m types of data. Then the data collected by all sensor nodes in each time slot is is a real number domain; after time t = p × τ, a total of n × m × p multi-parameter data are transmitted to the base station, and the multi-parameter data can form an m-order tensor p represents the number of time slots during the monitoring period; the data collected in the i-th time slot, i.e., the tensor The i-th front slice of It can be expressed as:

[0044]

[0045] Among them, f(N j ,A k ,i) represents the sensor node N j A sensed at the i-th time slot k Type data, j = 1, 2, ..., n, k = 1, 2, ..., m;

[0046] Using the sparse sampling method, a certain proportion ρ of sensor nodes are randomly selected for sampling, and transmitted to the base station in real time through multi-hop, ρ is the sampling ratio and 0<ρ<<1; the partial sampling data received by the base station is the actual number of samples, represents rounding down, and d is the sampling operator Acting on M, we get: d = Ω(M), and record the position of d in M ​​as the index position; by the sparse sampling method, we can get that the data tensor received by the base station in continuous time slots is as follows Figure 1 As shown;

[0047] Step 2: Use the sliding window model to introduce historical data into the current window, update the data tensor of the current window, and obtain the data tensor of the current window.

[0048] like Figure 2 As shown, two adjacent windows with a fixed width of w time slots are shown, T c represents the current time slot; along the time slot axis, the previous window of the current window contains the time slot T c-w ~T c-1 The reconstructed multi-parameter data, the current window contains the time slot T c-w+1 ~T c The collected data; the data in each window can form an m-order tensor The window slides one time slot each time, that is, time slot T c-w The data is removed from the window, and the current time slot T c The data enters the window, the data tensor in the window is updated, and the current window data tensor is obtained. From a mathematical point of view, the current window data tensor Can be divided into and M c Two parts, including For historical data, is the current time slot data, i.e., the multi-parameter data collected in the current time slot;

[0049] Step 3: To achieve real-time reconstruction of data, the spatial subspace of the current time slot data is obtained from the historical data based on Tucker decomposition, and the reconstruction of the current time slot data is converted into the solution of equation (4);

[0050] Based on Tucker decomposition, the current window data tensor Can be decomposed into:

[0051]

[0052] Among them, the factor matrix and It can be regarded as the spatial distribution subspace, multi-parameter distribution subspace and time distribution subspace of the current window tensor data; G (1) That is, the spatial subspace of the current time slot data; the core tensor represents the interaction level of each subspace;

[0053] The 1-mode matrix of formula (2) is:

[0054]

[0055] in, Represents the core tensor The 1-mode matrix of represents the Kronecker product;

[0056] According to the sliding window model, the 1-mode matrixed data of the current window data tensor can also be expressed as [HM c ], For historical data 1-mode matrixization of ;

[0057] make G (1) =G,C (1) =C; Based on matrix decomposition, the matrix Φ is decomposed into Φ h , Φ c ,in Then Φ=[Φ h Φ c ], so [HM c ]=GC[Φ h Φ c ], where H = GCΦ h , M c =GCΦ c ; Let S = GC, then [HM c ]=S[Φ h Φ c ], so the matrix H is decomposed to get the matrix S. The base station reconstructs the current time slot data in real time through the received partial sampling data d and the constrained total variation in the time and space directions, that is, solves the following equation:

[0058]

[0059] in, represents the reconstructed data matrix, |||| 1 、|||| 2 denote the 1-norm and 2-norm respectively, λ and μ are regularization parameters, Represents the current window data tensor The current time slot data and the previous time slot data in ▽ v The operation is defined as: v (SΦ c )=(SΦ c ) j+1,k -(SΦ c ) j,k , represents the matrix SΦ cThe difference between the element in the j+1th row and the kth column and the element in the jth row and the kth column; ▽ l The operation is defined as: l [H c-1 ; SΦ c ]=SΦ c -H c-1 , represents the difference between the corresponding position elements of the current time slot data and the previous time slot data;

[0060] Step 4: Convert the solution of equation (4) into the solution of the following constraint equation:

[0061]

[0062] The augmented Lagrangian function of formula (5) is:

[0063]

[0064] In formula (6), A and B are Lagrange multipliers, α and β are penalty coefficients;

[0065] Step 5: Use the alternating direction multiplication method to solve equation (6) and obtain the matrix Φ c , through M c =SΦ c Reconstruct current time slot data;

[0066] Step 6. Replace the data at the corresponding position in the current time slot data reconstructed in step 5 with the received partial sampling data d according to the index position to obtain the replaced current time slot data. Use the replaced current time slot data as the historical data for reconstructing the next time slot data, and then repeat steps 3 to 6 to realize real-time reconstruction of multi-parameter data.

[0067] In order to verify the effectiveness of the proposed method in reconstructing multi-parameter data, three methods including vector method (Seq-Prog-CS), matrix method (CSMC) and conventional tensor methodology (tensor methodology) in the prior art are selected for comparison. Proposed represents the proposed method. Multi-parameter data collected by Berkeley Research Laboratory are selected as test data. Since data loss in the network is inevitable, a small and complete data subset is selected as the real test data. Specifically, the original data contains three parameter data including temperature, humidity and voltage sensed by 49 sensor nodes in 130 time slots. Since sparse sampling is used to reduce energy consumption, only part of the sampled data is used in each time slot. can be successfully transmitted to the base station; the sampling ratio ρ is used to represent the ratio of the number of sampled data to the total amount of data, that is, the current time slot data M c The number of elements in; select the 50th time slot as the first current time slot, that is, The current time slot data is reconstructed for the first time. The data of the next 80 time slots are sparsely sampled in sequence, starting from the first current time slot. The index of the sampled data in the current time slot is the same in all algorithms. The method of the present invention and the conventional tensor method are used to reconstruct multi-parameter data respectively, and the vector method and the matrix method are used to reconstruct each parameter data respectively. The reconstruction error is characterized by the normalized mean absolute error (NMAE), and the definition of NMAE is:

[0068]

[0069] In formula (7), M c are the current time slot data of the reconstructed and real test data respectively, Π represents the sampling index subset of the complete entry set, that is, only the reconstruction error of the missing data is considered when calculating NMAE.

[0070] The matrix method and tensor method only calculate the NMAE of the current time slot data in the current window; for each method, the random sampling and reconstruction process are repeated 10 times, and the average NMAE is calculated. The optimal regularization parameter of each method is selected individually to ensure that the experimental results are convincing. In the experiment, the window width w=5 of the present invention. Figures 3 to 5 are error comparison diagrams of the present invention and the existing method for reconstructing multi-parameter data at different sampling ratios, wherein Figures 3 (a) to (c) are the errors obtained by reconstructing temperature, humidity and voltage with a sampling ratio of 0.1; Figures 4 (a) to (c) are the errors obtained by reconstructing temperature, humidity and voltage with a sampling ratio of 0.2; Figures 5 (a) to (c) are the errors obtained by reconstructing temperature, humidity and voltage with a sampling ratio of 0.3.

[0071] It can be seen from the figure that under the same sampling ratio and different sampling ratios, the reconstruction error of multi-parameter data using the method of the present invention is generally smaller than that of the existing method, which improves the accuracy of real-time multi-parameter data reconstruction; and when the number of reconstruction time slots is greater than 5, that is, the historical data are all previously reconstructed data, the reconstruction accuracy of the present invention still maintains a low error.

[0072] There are three reasons why the reconstruction error of the present application method is small: first, because the multi-parameter data is organized into tensor form, the spatiotemporal correlation between the multi-parameter data and the intrinsic relationship between various types of data are fully utilized; second, the spatial distribution subspace of the current time slot data is obtained from the historical data, which retains the spatiotemporal correlation of the data; third, the base station reconstructs the current time slot data in real time through the received partial sampling data and combined with the constrained total variation in the spatiotemporal direction. In addition, the vector method, matrix method and conventional tensor method all reconstruct the data after transmitting all the time slot data to the base station together, while the method of the present invention reconstructs the data once after transmitting the current time slot data to the base station to achieve real-time reconstruction of the data, fast data processing speed, and only part of the sampling data is transmitted to the base station in each time slot, which reduces the energy consumption required for sensor nodes to collect and transmit data.

[0073] Any matters not described in the present invention are applicable to the prior art.

Claims

1. A subspace-based real-time reconstruction method for multi-parameter data of the Internet of Things, characterized in that: The method comprises the following steps: Step 1: In each time slot, sensor nodes are randomly selected for sampling according to the sampling ratio, and the sampled data is transmitted to the base station. The base station receives part of the sampled data. is the field of real numbers, is the actual number of samples, represents rounding down, n is the number of sensor nodes, m is the total number of data types, ρ is the sampling ratio and 0<ρ<<1; Step 2: Use the sliding window model to introduce historical data into the current window, update the data tensor of the current window, and obtain the current window data tensor. w is the sliding window width; the current window data tensor Contains historical data and the current time slot data M c Two parts; Step 3: Based on Tucker decomposition, the spatial subspace of the current time slot data is obtained from the historical data, and the reconstruction of the current time slot data is converted into the solution formula (4); Based on Tucker decomposition, the current window data tensor This breaks down into: Among them, the factor matrix G (1) , G (2) and G (3) is the spatial distribution subspace, multi-parameter distribution subspace and time distribution subspace of the tensor data in the current window; G (1) That is, the spatial subspace of the current time slot data; the core tensor represents the interaction level of each subspace; The 1-mode matrix of formula (2) is: Among them, C (1) Represents the kernel tensor The 1-mode matrix of represents the Kronecker product; According to the sliding window model, the 1-mode matrixed data of the current window data tensor can be expressed as [HM c ], H is the historical data 1-mode matrixization of ; make G (1) =G,C (1) =C; Based on matrix decomposition, the matrix Φ is decomposed into Φ h , Φ c , then [HM c ]=GC[Φ h Φ c ], where H = GCΦ h , M c =GCΦ c ; Let S = GC, so the matrix H is decomposed to get the matrix S. The base station reconstructs the current time slot data in real time through the received partial sampling data d and the constrained total variation in the time and space directions, that is, solves the following equation: M c =SΦ c in, represents the reconstructed data matrix, || ||1 and || ||2 represent the 1-norm and 2-norm respectively, λ and μ are regularization parameters, Represents the current window data tensor The current time slot data and the previous time slot data in ; The operation is defined as: Denotes the matrix SΦ c The difference between the element in the j+1th row and the kth column and the element in the jth row and the kth column; The operation is defined as: Indicates the difference between the corresponding position elements of the current time slot data and the previous time slot data; Step 4: Convert the solution of equation (4) into the solution of the following constraint equation: The augmented Lagrangian function of formula (5) is: In formula (6), A and B are Lagrange multipliers, α and β are penalty coefficients; Step 5: Use the alternating direction multiplication method to solve equation (6) and obtain the matrix Φ c , through M c =SΦ c Reconstruct current time slot data; Step 6. Replace the data at the corresponding position in the current time slot data reconstructed in step 5 with the received partial sampling data d according to the index position to obtain the replaced current time slot data. Use the replaced current time slot data as the historical data for reconstructing the next time slot data, and then repeat steps 3 to 6 to realize real-time reconstruction of multi-parameter data.

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