Sampling rate control method and system for multi-mode sensing system

Abstract

The invention relates to a sampling rate control method for a multi-mode sensing system. The sampling rate control method comprises the following steps: a plurality of sensors continuously send data packets to receiving end equipment according to sampling rates of the sensors; the receiving end device calculates the average information age of all sensors in a control period according to the received data packet, and determines the updated sampling rate of the plurality of sensors in the next control period based on a pseudo Jacobian matrix and the average information age; and respectively sending the updated sampling rate in the next control period to the plurality of sensors, wherein the plurality of sensors continuously send data packets to receiving end equipment based on the updated sampling rate in the next control period. According to the method, differentiated AoI performance guarantee can be provided, and the sampling rate of the next period can be adaptively updated, so that when the network transmission delay statistics suddenly changes, the AoI convergence speed can be greatly improved, and the long-term system stability is kept.

Description

Technical Field

[0001] The present invention relates to the field of industrial Internet of Things, and more particularly, to a sampling rate control method and system for a multimodal sensing system. Background Art

[0002] In recent years, with the rapid development of industrial Internet of Things (IoT) technology, the integrated application of sensors in industrial monitoring, autonomous driving systems, and intelligent automation control has shown an exponential growth trend. In these industrial applications, sensors usually sample dynamic physical processes and generate status update data packets that need to be transmitted to the target terminal in real time. Such application scenarios place strict requirements on the timeliness of data transmission. Due to the low value of outdated status update data packets, quantitative indicators such as throughput and transmission delay in traditional network performance evaluation systems have inherent defects in evaluating the value of status update data. For example, maximizing throughput performance indicators often requires adopting a higher sampling rate, but at the same time it will cause network congestion. Although the system may maintain a higher throughput, the timeliness of the status update data packets cannot be guaranteed, thus losing their application value. To solve the above problems, Age of Information (AoI) has been proposed as a new performance evaluation indicator and has received widespread attention in academia [2]. This indicator defines the timeliness metric from the information receiving end, specifically defined as the time interval from the time when the last valid status update packet received was generated to the current time. Through the systematic optimization of AoI indicators, the real-time response capability of the state perception system in the Industrial Internet of Things can be significantly improved, which has important engineering value.

[0003] Sensor sampling strategies are key to optimizing AoI. Improper sampling rate settings can lead to dual risks: low-frequency sampling results in insufficient data, while high-frequency sampling causes queue congestion, both of which significantly degrade the system's AoI performance. Current technical solutions focus on single-modal sensing scenarios and do not differentiate the AoI requirements of different sensors. Due to the inherent limitations of single-modal sensing, multimodal sensing can significantly improve system perception capabilities by integrating data from multiple sensors. However, multimodal sensing introduces new technical challenges in the design of sampling schemes. Specifically, multimodal sensing systems typically involve multiple sensors with different AoI requirements and a shared transmitter. When these sensors share limited transmission resources, high-priority data streams are easily interfered with by low-priority data streams, resulting in a loss of critical information timeliness. This makes existing technologies difficult to apply in multimodal industrial scenarios. Achieving differentiated AoI assurance for multimodal sensor data has become a technical bottleneck that urgently needs to be overcome in the Industrial Internet of Things (IIoT).

[0004] Furthermore, with the large-scale deployment of intelligent terminals such as mobile robots, industrial communication networks are becoming significantly more dynamic. Actual transmission delays exhibit unknown and non-stationary characteristics, and their statistical distribution is difficult to predict. Existing research on sampling schemes typically assumes that this distribution is known or stationary. These assumptions allow for characterizing the relationship between sampling rate and AoI, and finding the optimal sampling rate to optimize AoI. However, this is not possible in unknown and non-stationary situations. Adding the need for multimodal sensor fusion makes the problem extremely challenging: it is necessary to ensure differentiated AoI indicators for different sensor data streams while also addressing the uncertain interference brought about by dynamic network environments. Existing literature has yet to effectively address this challenge.

[0005] In the currently used Zero Waiting with Maximum Age First (ZW-MAF) strategy, a sensor immediately samples and transmits a new packet when the previous packet completes transmission. Furthermore, the scheduler selects the sensor with the oldest information age for sampling and transmission. Notably, the ZW-MAF strategy requires an ACK for each packet transmission to achieve its zero-wait feature.

[0006] Therefore, current sensor signal sampling strategies usually have the following disadvantages.

[0007] Disadvantage 1: It's difficult to balance the diverse information age requirements of sensors. Existing research focuses on minimizing the sum of the long-term average information age of all sensors. However, different sensors have different information age requirements. Some sensors collecting critical data require a shorter information age, which cannot be achieved by minimizing the sum of all sensors' information ages. Furthermore, multimodal sensor data streams can interfere with each other during transmission. These factors make it difficult to balance the diverse information age requirements of sensors.

[0008] Disadvantage 2: The sampling rate is difficult to control when the transmission delay distribution is non-stationary. Sampling rate control is a prerequisite for ensuring information age. Existing research typically derives the mathematical relationship between information age and sampling rate under the assumption of a stationary and known transmission delay distribution, solving for the optimal sampling rate that minimizes information age. However, in highly dynamic industrial network environments, the transmission delay distribution is often unknown and non-stationary, making sampling rate control optimization very difficult. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to address the above-mentioned shortcomings of the prior art and provide a sampling rate control method and system for a multimodal sensing system. The method and system can provide differentiated AoI performance guarantees and adaptively update the sampling rate of the next cycle. This greatly improves the AoI convergence speed when network transmission delay statistics suddenly change, thereby maintaining long-term system stability.

[0010] The technical solution adopted by the present invention to solve the technical problem is to construct a sampling rate control method for a multimodal sensing system, comprising:

[0011] Multiple sensors continuously send data packets to the receiving device according to their sampling rate;

[0012] The receiving device calculates an average information age of all sensors in a control cycle based on the received data packets, and determines an update sampling rate of the multiple sensors in a next control cycle based on the pseudo-Jacobian matrix and the average information age; wherein the one control cycle is defined as the receiving device receiving N data packets from the multiple sensors, where N is a positive integer;

[0013] The updated sampling rate in the next control cycle is sent to the multiple sensors respectively, and the multiple sensors continuously send data packets to the receiving end device based on the updated sampling rate in the next control cycle.

[0014] In the sampling rate control method for a multimodal sensing system according to the present invention, the receiving device calculates the average information age of all sensors in a control cycle based on received data packets, and determines the update sampling rates of the multiple sensors in the next control cycle based on the pseudo-Jacobian matrix and the average information age, including:

[0015] Based on the receiving time and generating time of each sensor’s data packet, the average information age of each sensor in a control cycle is calculated;

[0016] Calculating an optimal solution for the sampling rates of the multiple sensors in a next control cycle based on the average information age, the sampling rate, and the pseudo-Jacobian matrix;

[0017] An update sampling rate of the plurality of sensors in a next control cycle is determined based on the sampling rate optimal solution and the delay constraint matrix.

[0018] In the sampling rate control method for a multimodal sensing system according to the present invention, the calculation of the average information age of each sensor within a control period based on the reception time and generation time of the data packet of each sensor includes:

[0019] The average information age of the c-th sensor in the k-th control cycle is calculated based on the following formula:

[0020]

[0021] Among them, a c,k represents the average information age of sensor c in the kth control cycle, a c (t) represents the instantaneous information age of sensor c at time t, n c,k represents the number of data packets from sensor c successfully received in the kth control cycle, Y c,k,j represents the system time of the jth data packet of sensor c successfully received in the kth control cycle, X c,k,j represents the time interval between the adjacent data packets of sensor c that are successfully received in the kth control cycle; Y c,k,j-1 The system time of the j-1th data packet of sensor c that is successfully received in the kth control cycle; Indicates the nth sensor c successfully received in the kth control cycle c,k The reception time of a data packet, The sensor c nth signal successfully received in the k-1th control cycle c,k-1 The reception time of a data packet.

[0022] In the sampling rate control method for a multimodal sensing system according to the present invention, the step of calculating the optimal sampling rate solution for the multiple sensors in the next control period based on the average information age, the sampling rate, and the pseudo-Jacobian matrix includes:

[0023] Obtaining an average information age vector sequence of all sensors in the kth control cycle based on the average information age of each sensor;

[0024] Based on minimizing the average information age violation probability, establishing a mathematical expression between the average information age vector sequence and the sampling rate vector sequence of all sensors;

[0025] An optimal solution sequence of sampling rates of the multiple sensors in a next control cycle is obtained based on the mean information age vector sequence, the pseudo-Jacobian matrix, and the sampling rate vector sequence.

[0026] In the sampling rate control method for a multimodal sensing system according to the present invention, the mathematical expression between the average information age vector sequence and the sampling rate vector sequence of all sensors is:

[0027]

[0028] stu k ←u1,…,uk-1 ,a1,…,a k-1

[0029] Among them, a k =(a 1,k ,…,a c,k ) T ,u k =(u 1,k ,…,u C,k ) T ,δ=(δ1,…,δ C ) T ;a 1,k represents the average information age of sensor 1 in the kth control cycle, a C,k The average information age of sensor C in the kth control cycle, u 1,k represents the sampling rate of sensor 1 in the kth control cycle, u C,k represents the sampling rate of sensor C in the kth control cycle; δ1 represents the average information age threshold of sensor 1, δ represents the average information age threshold vector sequence of all sensors, K represents the number of control cycles, C represents the number of sensors, c∈C, Indicates a violation indicator. is equal to 0 when , and equal to 1 otherwise.

[0030] In the sampling rate control method for a multimodal sensing system according to the present invention, obtaining the optimal sampling rate solution sequence of the multiple sensors in the next control period based on the mean information age vector sequence, the pseudo-Jacobian matrix, and the sampling rate vector sequence includes:

[0031] The multimodal sensing system is transformed into the following equivalent dynamic linear data model Δa k =V k Δu k ,; where Δu k =u k -u k-1 , Δa k =a k -a k-1 , V k =[v ij,k ] c×C And represents the time-varying C-order pseudo-Jacobian matrix in the k-th control period, whose elements are all bounded quantities and the signs of the elements remain unchanged in different control periods;

[0032] The estimation formula for the time-varying C-order pseudo-Jacobian matrix is obtained as follows:

[0033]

[0034] in, Indicates V k The estimated value of represents the time-varying C-order pseudo-Jacobian matrix V in the k-1th control cycle k-1 The estimated value of; μ represents the weight parameter; Δa k-1 =a k-1 -a k-2 ;Δu k-1 =u k-1 -u k-2 ;a k-1 represents the average information age vector sequence of all sensors in the k-1th control cycle, a k-2 represents the average information age vector sequence of all sensors in the k-2th control cycle; u k-1 represents the sampling rate vector sequence of all sensors in the k-1th control cycle; u k-2 represents the sampling rate vector sequence of all sensors of all sensors in the k-2th control cycle;

[0035] Based on the estimated value of the time-varying C-order pseudo-Jacobian matrix The average information age threshold vector sequence δ of all sensors, the sampling rate vector sequence u of all sensors in the k-1th control cycle k-1 , the average information age vector sequence a of all sensors in the k-1th control cycle k-1 Calculate the sampling rate vector sequence u of all sensors in the kth control cycle k As the optimal solution sequence of the sampling rates of the multiple sensors in the next control cycle:

[0036]

[0037] in λ represents the weight parameter, And it is the identity matrix.

[0038] In the sampling rate control method for a multimodal sensing system described in the present invention, if or or if

[0039] Where V0=[v ij,0 ] c×C is the initial time-varying C-order pseudo-Jacobian matrix, θ1, θ2 are positive constants, satisfying the relationship ρ≥1, θ2>θ1(2ρ+1)(C-1).

[0040] In the sampling rate control method for a multimodal sensing system according to the present invention, determining the update sampling rates of the multiple sensors in the next control cycle based on the sampling rate optimal solution and the delay constraint matrix includes:

[0041] The delay constraint matrix is obtained based on the packet loss rate, the average transmission delay, the second-order moment of the transmission delay, the average information age vector sequence, the pseudo-Jacobian matrix, and the sampling rate vector sequence.

[0042] when When it is established, the optimal solution sequence u of the sampling rate k As the update sampling rate of the multiple sensors in the next control cycle, otherwise u k =x k [1:C] is the update sampling rate of the multiple sensors in the next control cycle, where:

[0043]

[0044] Where min_index represents the index of the sensor with the smallest average information age threshold; λ represents the weight parameter, and is the identity matrix; Indicates V k The estimated value of a k-1 represents the average information age vector sequence of all sensors in the k-1th control cycle, u k-1 represents the sampling rate vector sequence of all sensors of all sensors in the k-1th control cycle, and δ represents the average information age threshold vector sequence of all sensors.

[0045] In the sampling rate control method for a multimodal sensing system according to the present invention, the delay constraint matrix is a symmetric matrix with the main diagonal elements being The remaining off-diagonal elements are They represent the estimated packet loss rate in the kth control cycle, the average transmission delay of N data packets, and the second-order moment of the average transmission delay of N data packets.

[0046] Another technical solution adopted by the present invention to solve its technical problem is to construct a sampling rate control system for a multimodal sensing system, including: multiple sensors, a transmitting end device and a receiving end device, wherein the transmitting end device and the receiving end device store computer programs for executing the sampling rate control method for the multimodal sensing system.

[0047] The sampling rate control method and system for a multimodal sensing system of the present invention utilizes only the real-time sampling rate and average AoI to update the PJM and determine the sampling rate of all sensors in each control cycle. A dynamic update step size is used to update the sampling rate, providing differentiated AoI performance guarantees and adaptively updating the sampling rate for the next cycle. Furthermore, the strategy converges quickly when delay statistics change, significantly improving the AoI convergence speed and thus maintaining long-term system stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0049] Figure 1 1 is a flow chart of a sampling rate control method for a multimodal sensing system according to the present invention;

[0050] Figure 2 The variation of the age of information (AoI) of each sensor in different control cycles is shown;

[0051] Figure 3 The software algorithm of the sampling rate control method for a multimodal sensing system of the present invention is shown;

[0052] Figure 4 It is a principle block diagram of the sampling rate control system for the multimodal sensing system of the present invention;

[0053] Figure 5 1. It is a schematic diagram of the change of the simulated ST-AoI of the sensor when the sampling rate control method for the multimodal sensing system of the present invention and the prior art are applied to a multimodal sensing system with two sensors;

[0054] Figure 6 1 is a schematic diagram of the actual ST-AoI changes of sensors when the sampling rate control method for a multimodal sensing system of the present invention and the prior art are applied to a multimodal sensing system with two sensors. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0056] Figure 1 FIG. 1 is a flow chart of a sampling rate control method for a multi-modal sensing system according to the present invention. Figure 1As shown, in step S1, multiple sensors continuously send data packets to the receiving device according to their sampling rates. In a preferred embodiment of the present invention, the sampling rate control method for a multimodal sensing system of the present invention can be applied to a point-to-point multimodal sensing communication system composed of C sensors and a shared transmitter, using sub-index To represent different sensors. Where c represents the number of the sensor, that is, sensor c represents the cth sensor, c and The values of are all positive integers.

[0057] In a preferred embodiment of the present invention, the data packets generated by each sensor are pushed into a First-In-First-Out (FIFO) queue and transmitted to a remote receiving device, such as a monitor or control cycle, via a wireless network. Assuming that each sensor can adjust its sampling rate, the generation of status update data packets follows a Poisson process. The model considered by the present invention can represent various industrial terminal devices equipped with multiple sensors, such as intelligent robots. Since industrial wireless networks are usually highly dynamic, the distribution of transmission delay and packet loss rate is usually unknown and non-stationary. To overcome this, the present invention adopts a general piecewise stationary model to represent the distribution of transmission delay and packet loss rate, in which the distribution can change arbitrarily. The present invention has no further assumptions about a specific distribution model or change pattern, so it can be applied to various practical dynamic networks.

[0058] In step S2, the receiving device calculates the average information age of all sensors in a control cycle based on the received data packets, and determines the update sampling rate of the multiple sensors in the next control cycle based on the pseudo-Jacobian matrix and the average information age; wherein the one control cycle is defined as the receiving device receiving N data packets from the multiple sensors, where N is a positive integer.

[0059] In a preferred embodiment of the present invention, in order to adjust the sampling rate of all sensors in a dynamic wireless network, it is assumed that the sampling rate is adjusted cycle by cycle with a sub-index k, where each control cycle is defined as the receiving device successfully receiving N data packets from all sensors, where the value of N is a positive integer.

[0060] In a preferred embodiment of the present invention, first, the average information age of each sensor in a control cycle is calculated based on the reception time and generation time of the data packet of each sensor; then, the optimal solution of the sampling rate of the multiple sensors in the next control cycle is calculated based on the average information age, the sampling rate, and the pseudo-Jacobian matrix; then, based on the optimal solution of the sampling rate and the delay constraint matrix, the update sampling rate of the multiple sensors in the next control cycle is determined.

[0061] In step S3, the updated sampling rate in the next control cycle is sent to the multiple sensors respectively, and the multiple sensors continuously send data packets to the receiving end device based on the updated sampling rate in the next control cycle.

[0062] In the present invention, at the end of each control cycle, the receiving device updates the sampling rate of all sensors The vector is fed back to each sensor to adjust the sampling rate; the multiple sensors continuously send data packets to the receiving end device based on the updated sampling rate.

[0063] Figure 2 The variation of the age of information (AoI) of each sensor in different control cycles is shown. Figure 3 The software algorithm of the sampling rate control method for the multi-modal sensing system of the present invention is shown. Figures 2-3 The sampling rate control process of the sampling rate control method for a multimodal sensing system of the present invention, namely, the receiving device calculates the average information age of all sensors in a control cycle based on the received data packets, and determines the update sampling rates of the multiple sensors in the next control cycle based on the pseudo-Jacobian matrix and the average information age, is described as follows.

[0064] First, based on the reception time and generation time of each sensor's data packet, the average information age of each sensor in a control cycle is calculated. Since the sensor data needs to ensure the freshness of information, in the preferred embodiment of the present invention, the AoI is used to measure the freshness of information. In order to obtain the average AoI of each sensor in different control cycles, the n c,k is defined as the number of data packets from sensor c that are successfully received in the kth control cycle, where C represents the number of sensors, c∈C. Figure 2 As shown, for the cth sensor, that is, sensor c; Y c,k,j represents the system time of the jth data packet of sensor c successfully received in the kth control cycle, X c,k,j represents the time interval between the adjacent data packets of sensor c that are successfully received in the kth control cycle; Y c,k,j-1 The system time of the j-1th data packet of sensor c successfully received in the kth control cycle, where j = 1, 2, ..., n c,k .make and Denotes the index of the most recently received state update, R c,k,j represents the receiving time of the data packet of sensor c that is successfully received in the kth control cycle, G c,k,jThe generation time of the data packet of sensor c that is successfully received in the kth control cycle; the instantaneous AoI of sensor c at time t is defined as

[0065] a c (t) = tG c,k(t),j(t) (1)

[0066] like Figure 2 As shown, in order to calculate the average AoI of sensor c in each control cycle, as mentioned above, Y c,k,j represents the system time of the jth data packet of sensor c successfully received in the kth control cycle, X c,k,j represents the time interval between the adjacent data packets of sensor c that are successfully received in the kth control cycle; Based on these definitions, the area Q c,k,j The average AoI of sensor c in the kth control cycle can be obtained, which is expressed as:

[0067]

[0068]

[0069] in is the system time of the last successfully received sensor c data packet in the previous control cycle; where a c,k represents the average information age of sensor c in the kth control cycle, a c (t) represents the instantaneous information age of sensor c at time t, n c,k represents the number of data packets from sensor c successfully received in the kth control cycle, Y c,k,j represents the system time of the jth data packet of sensor c successfully received in the kth control cycle, X c,k,j represents the time interval between the adjacent data packets of sensor c that are successfully received in the kth control cycle; Y c,k,j-1 The system time of the j-1th data packet of sensor c that is successfully received in the kth control cycle; Indicates the nth sensor c successfully received in the kth control cycle c,k The reception time of a data packet, The sensor c nth signal successfully received in the k-1th control cycle c,k-1 Based on formula (2), only the reception time R of each sensor c data packet is used. c,k,j and generation time G c,k,j , the receiving device can calculate a in each control cycle c,k ; where R c,k,j Can be obtained directly at the receiving end, G c,k,jIt can be read from the payload of the data packet. Here, the letters used as sequence numbers or indexes, such as j, k, c, etc., are all positive integers.

[0070] Existing sampling strategy research often assumes a stationary transmission delay distribution, aiming to minimize the sum of the long-term average AoI of all sensors in a multimodal sensing system. However, network transmission delays can vary dramatically due to factors such as robot motion and traffic load fluctuations, and the transmission delay distribution in practical systems often exhibits unknown and non-stationary characteristics. Therefore, in dynamic network environments, the optimization of the short-term age of information (ST-AoI) should be emphasized. ST-AoI can be represented by the average AoI per control cycle and effectively characterizes the system's real-time state update performance. This is because even if the system's long-term average AoI remains low, ST-AoI may still exhibit significant peaks, which can lead to inability to guarantee the quality of service for real-time applications in dynamic network environments.

[0071] In addition, in the multimodal sensing communication system under consideration, the AoI requirements of various types of sensors may vary significantly, and the existing research that aims to minimize the sum of average AoIs cannot achieve this requirement. According to the specific application requirements, it is very important to ensure that the ST-AoI of each sensor is lower than different ST-AoI thresholds. In order to achieve this goal, the present application obtains the average information age vector sequence of all sensors in the kth control cycle based on the average information age of each sensor; based on minimizing the probability of violation of the average information age, a mathematical expression between the average information age vector sequence and the sampling rate vector sequence of all sensors is established; based on the average information age vector sequence, the pseudo-Jacobian matrix, and the sampling rate vector sequence, the optimal solution sequence of the sampling rates of the multiple sensors in the next control cycle is obtained, as follows.

[0072] Set δ=(δ1,…,δ C ) T It is defined as the ST-AoI requirement threshold (i.e., average AoI) of different sensors. For the sake of mathematical simplicity, let a k =(a 1,k ,…,a C,k ) T ,u k =(u 1,k ,…,u C,k ) T , this application constructs the following problem to minimize the ST-AoI violation probability, which is mathematically expressed as follows

[0073]

[0074] stu k←y1,…,u k-1 ,a1,…,a k-1 (3).

[0075] Among them, a k =(a 1,k ,…,a c,k ) T ,u k =(u 1,k ,…,u C,k ) T ,δ=(δ1,…,δ C ) T ;a 1,k represents the average information age of sensor 1 in the kth control cycle, a C,k represents the average information age of sensor C in the kth control cycle, u 1,k represents the sampling rate of sensor 1 in the kth control cycle, u C,k represents the sampling rate of sensor C in the kth control cycle; δ1 represents the average information age threshold of sensor 1, δ represents the average information age threshold vector sequence of all sensors, K represents the number of control cycles, C represents the number of sensors, c∈C, Indicates a violation indicator. It is equal to 0 when , and equal to 1 otherwise. It is worth noting that when the distribution of transmission delay and packet loss rate is unknown and non-stationary, the optimization objective has no clear form and it is challenging to solve the optimal sampling rate.

[0076] Based on this, this application proposes a Differentiated AoI Guaranteed Sampling (DAGS) strategy for unknown and non-stationary delayed statistical multimodal sensing systems to reduce the ST-AoI violation probability of the multimodal sensing system. This patent first introduces a dynamic linearized data model to characterize the a k and u k The relationship between the two can be determined by estimating the Pseudo Jacobian Matrix (PJM), based on a k and u k The DAGS strategy of this application dynamically adjusts the sampling rate of sensors to ensure the differentiated AoI requirements of different sensors. In this application, based on the average information age vector sequence, the pseudo-Jacobian matrix, and the sampling rate vector sequence, the optimal sampling rate solution sequence for the multiple sensors in the next control cycle is obtained, as follows.

[0077] The multimodal sensing system with unknown and non-stationary delay statistics is transformed into the following equivalent dynamic linear data model:

[0078] Δa k =V k Δu k , (4)

[0079] where Δu j =u k -u j-1 , Δa k =a k -a k-1 , V k =[v ij,k ] c×C And represents the time-varying C-order pseudo Jacobian matrix (PJM) in the k-th control cycle, whose elements are all bounded quantities and the element signs remain unchanged in different control cycles. For the equivalent data model given by formula (4), the a of the multimodal sensor system is k and u k The implicit relationship between Δu k and Δa k By time-varying PJMV k Revealed. In addition, V k The change of can effectively represent all unknown characteristics of the non-stationary delay statistics. The estimation formula for obtaining the time-varying C-order pseudo-Jacobian matrix is as follows:

[0080]

[0081] in, Indicates V k The estimated value of represents the time-varying C-order pseudo-Jacobian matrix V in the k-1th control cycle k-1 The estimated value of; μ represents the weight parameter; Δa k-1 =a k-1 -a k-2 ;Δu k-1 =u k-1 -u k-2 ;a k-1 represents the average information age vector sequence of all sensors in the k-1th control cycle, a k-2 represents the average information age vector sequence of all sensors in the k-2th control cycle; u k-1 represents the sampling rate vector sequence of all sensors in the k-1th control cycle; u k-2 represents the sampling rate vector sequence of all sensors of all sensors in the k-2th control cycle.

[0082] When the network dynamics change dramatically, the estimated values of PJM elements may exceed the set range and their signs may change. To improve the estimation performance and ensure stability, the following reset scheme is used:

[0083]

[0084] Where V0=[v ij,0 ] C×C is the initial time-varying C-order pseudo-Jacobian matrix, θ1, θ2 are positive constants, satisfying the relationship ρ≥1, θ2>θ1(2ρ+1)(C-1). This shows that PJM is a diagonally dominant matrix. Condition and Ensure that the signs of the elements of the PJM remain unchanged across different control cycles.

[0085] Then, based on the estimated value of the time-varying C-order pseudo-Jacobian matrix The average information age threshold vector sequence δ of all sensors, the sampling rate vector sequence u of all sensors in the k-1th control cycle k-1 , the average information age vector sequence a of all sensors in the k-1th control cycle k-1 Calculate the sampling rate vector sequence u of all sensors in the kth control cycle k As the optimal solution sequence of the sampling rates of the multiple sensors in the next control cycle:

[0086]

[0087] in λ represents the weight parameter, And it is the identity matrix.

[0088] Then, based on the optimal solution of the sampling rate and the delay constraint matrix, the updated sampling rates of the multiple sensors in the next control cycle are determined. Figure 3 As shown in the figure, in each control cycle in which N data packets are successfully received, the receiving device calculates the average AoIa of all sensors in the cycle based only on the received data packets. k ( Figure 3 Line 24); and estimate the delay statistics to obtain the constraint coefficient matrix ( Figure 3 Line No. 25), is a symmetric matrix with the main diagonal elements being The remaining off-diagonal elements are in, They represent the estimated packet loss rate in the kth control cycle, the average transmission delay of N data packets, and the second-order moment of the average transmission delay of N data packets. The specific calculation process is as follows:

[0089]

[0090] Where 0≤α≤1 is the weight factor, Indicates the total sampling rate, S k,j =R k,j -max(G k,j ,R k,j-1 ) represents the transmission delay of each received data packet. The receiving device can estimate the delay statistics using the N data packets received in each control cycle.

[0091] On this basis, the receiving device updates the PJM ( Figure 3 Numbered lines 6-12), according to PJM, the receiving device determines the sampling rate u of all sensors k ( Figure 3 Specifically, the receiving end first calculates the optimal sampling rate solution ( Figure 3 Line 14), if the constraint Established (line number 16, where 1 C is a C-dimensional all-one vector), the solution is determined as the sampling rate of all sensors; otherwise, the receiving device will solve it numerically ( Figure 3 The sampling rate is determined by the numbered lines 17-20, where min_index in line 18 represents the index of the sensor with the smallest ST-AoI requirement threshold, for example, the ST-AoI requirement δ of sensor c c Minimum, then take The coefficient of the cth row is The sink device then feeds the updated sampling rate back to the source and waits for the next control cycle to be triggered.

[0092] That is, in the present invention, when When it is established, the optimal solution sequence u of the sampling rate k As the update sampling rate of the multiple sensors in the next control cycle, otherwise u k =x k [1:C] is the update sampling rate of the multiple sensors in the next control cycle, where:

[0093]

[0094] Where min_index represents the index of the sensor with the smallest average information age threshold; λ represents the weight parameter, and is the identity matrix; Indicates V k The estimated value of a k-1 represents the average information age vector sequence of all sensors in the k-1th control cycle, u k-1 represents the sampling rate vector sequence of all sensors of all sensors in the k-1th control cycle, and δ represents the average information age threshold vector sequence of all sensors.

[0095] at last, Figure 3 Initialization parameters Δu0, Δa0, V0, The main diagonal elements of V0 can be obtained by randomly setting the sampling rate in the first two control cycles. The remaining elements can be manually set to the same value which is much smaller than the main diagonal element.

[0096] As can be seen, the sampling rate control method for multimodal sensing systems of the present invention does not rely on any prior information about non-stationary delay statistics. It only uses the real-time sampling rate and average AoI to update the PJM and determine the sampling rate of all sensors in each control cycle. Furthermore, the sampling rate control method for multimodal sensing systems of the present invention uses a dynamic update step size to update the sampling rate. This strategy can converge quickly when the delay statistics change, and is therefore implemented in practical connections (such as TCP and UDP).

[0097] Therefore, the sampling rate control method for multimodal sensing systems of the present invention only uses the real-time sampling rate and average AoI to update the PJM and determine the sampling rate of all sensors in each control cycle. It also adopts a dynamic update step to update the sampling rate, providing differentiated AoI performance guarantees and adaptively updating the sampling rate of the next cycle. When the delay statistics change, this strategy can converge quickly, which can greatly improve the convergence speed of AoI and thus maintain long-term system stability.

[0098] In a preferred embodiment of the present invention, the sampling rate control method for a multimodal sensing system can be directly deployed on a micro-host in an industrial IoT environment. A simple deployment procedure is as follows. At least two micro-hosts are required: one serving as a receiving device to receive data packets and the other as a transmitting device to send data packets. The transmitting device can be equipped with a variety of sensors to collect data, and data transmission can be carried out via UDP / TCP connections and Wi-Fi. The two micro-hosts require system clock synchronization. All sensors on the transmitting device are initialized by running two control cycles at two random sampling rates. Two different sampling rates can be manually specified. During a control cycle, the transmitting device continuously sends data packets to the receiving device based on the sampling rate. After receiving N data packets, the receiving device calculates the AoI of all sensors within that control cycle. It then calculates the sampling rate of all sensors for the next cycle and feeds the result back to the receiving device. The receiving device then adjusts the sampling rate of all sensors to keep the ST-AoI of each sensor below a preset threshold.

[0099] Therefore, the present invention also discloses a sampling rate control system for a multi-modal sensing system, which Figure 4 As shown. Multiple sensors, a transmitting device and a receiving device, as mentioned above, the transmitting device can be an industrial device, which can be equipped with multiple sensors to collect data. Data transmission can be carried out using UDP / TCP connection and transmitted via WIFI. The transmitting device and the receiving device need to synchronize the system clocks. All sensors of the transmitting device run two control cycles at two random sampling rates for initialization, and two different sampling rates can be manually specified. In one control cycle, multiple sensors continuously send data packets to the receiving device according to their sampling rates, and the transmitting device continuously sends data packets to the receiving device according to the sampling rate. After receiving N data packets, the receiving device calculates the AoI of all sensors in the control cycle, and then calculates the sampling rate of all sensors in the next cycle, and feeds the result back to the receiving device. The receiving device can adjust the sampling rate of all sensors so that the ST-AoI of each sensor is lower than the preset threshold. Here, the aforementioned sampling rate control method for a multimodal sensing system of the present invention can be used to calculate the sampling rate of all sensors in the next cycle.

[0100] To validate the sampling rate control method for multimodal sensing systems presented in this paper, we conducted the following simulations and comparisons using a Zero Waiting with Maximum Age First (ZW-MAF) strategy. In this ZW-MAF strategy, a sensor immediately samples and transmits a new packet when the previous packet completes transmission. Furthermore, the scheduler selects the sensor with the oldest information age for sampling and transmission among all sensors. Notably, the ZW-MAF strategy requires ACK feedback for each packet transmission to achieve its zero-wait feature.

[0101] In the simulation experiment, the sampling rate control method for the multimodal sensing system of the present invention is a multimodal sensing communication system with C=2 sensors. Assuming that each control cycle consists of N=2×10 4 The data packet is composed of , and the transmission delay in each control cycle is considered to obey the log-normal distribution, with a mean of m k , the variance is The packet loss rate of each control cycle is expressed as ε k In order to capture the non-steady-state delay statistics, this patent assumes that the parameter m k 、 ε k The control period remains unchanged in the continuous control period, and the control period changes from the interval [1ms, 10ms], [10ms] with a probability of 3% between different control periods. 2 , 300ms 2 ]、[10 -2 , 10 -4 ] changes uniformly. Figure 3 The weight parameters α, μ, λ, θ1, θ2, and ρ in the equation are set to 0.8, 10, and 10 respectively. -7 , 10 -3 , 10 -4 , 10 -2 , 10. The sampling rate control method for multimodal sensing systems of the present invention does not make any assumptions about non-stationary statistics and is therefore applicable to other distribution models. In addition, the sampling rate control method for multimodal sensing systems of the present invention simulates a total of 500 control cycles. The simulation results are shown in Figure 2. Figure 5 shown.

[0102] The sampling rate control method for a multimodal sensing system of the present invention sets the ST-AoI requirement thresholds of the two sensors to δ = (40, 100) ms respectively. Since the sampling rate control method for a multimodal sensing system of the present invention takes the mean square error (MSE) problem into consideration, this will cause the ST-AoI of the sensor to fluctuate around the desired target. In order to obtain better performance, the expected target of the sampling rate control method for a multimodal sensing system of the present invention can be set to 90% of the requirement threshold. It is worth noting that δ is a design parameter in the sampling rate control method for a multimodal sensing system of the present invention. From Figure 5 As can be seen from the figure, when the transmission delay and packet loss rate are unknown and non-stationary, the sampling rate control method for multimodal sensing systems of the present invention can meet the differentiated requirements of sensors within most control cycles. However, the ST-AoI of the existing ZW-MAF strategy can vary significantly due to drastic changes in transmission delay. Furthermore, ZW-MAF may not meet the expected goals because its goal is to minimize the sum of the average AoIs. In terms of the ST-AoI violation probability, the sampling rate control method for multimodal sensing systems of the present invention significantly outperforms the ZW-MAF strategy.

[0103] In a real-world system experiment, the sampling rate control method for a multimodal sensing system presented in this invention was implemented in a laboratory using three laptop computers, establishing an experimental platform via IEEE 802.11 interfaces and UDP connections. Two of the laptops established a multimodal sensing communication link, and one of them ran two UDP processes to represent two sensors. The other laptop randomly generated traffic within the [0, 0.8] Mbps range to simulate dynamic network changes. The experiment considered 100 control cycles, each consisting of N = 6000 data packets. All weight parameters of the sampling rate control method for a multimodal sensing system presented in this invention were identical to those given in the simulation experiment. Figure 6 The ST-AoI changes of two sensors in the actual system experimental scenario are described. The ST-AoI requirement thresholds of the two sensors are set to δ = (50, 30) ms respectively. Figure 6 As can be seen, the actual system experimental results are similar to the simulation results. Although the existing ZW-MAF strategy can achieve a relatively low ST-AoI, it cannot meet the strict requirements of sensor 2. More importantly, the sampling rate control method for multimodal sensing systems of the present invention can balance the sampling rates of different sensors according to differentiated requirements, thereby ensuring their ST-AoI under the different requirements of the two sensors. Compared with the ZW-MAF strategy, the sampling rate control method for multimodal sensing systems of the present invention can reduce the probability of ST-AoI violations in actual UDP connections from 51.6% to 4.3%.

[0104] The sampling rate control method for a multimodal sensing system of the present invention is oriented to a multimodal sensing system, can guarantee the differentiated AoI performance requirements of different sensors, and can be applied to actual communication systems with unknown and non-stationary delays. The sampling rate control method for a multimodal sensing system of the present invention does not require a priori assumptions or knowledge about transmission delay statistics, but instead uses a dynamic linearization data model to characterize the hidden relationship between the sampling rate and ST-AoI of all sensors. Based on this data model, the sampling rate control method for a multimodal sensing system of the present invention can adjust the sampling rates of all sensors to minimize the ST-AoI violation probability of the system. Simulation and actual system experimental results show that the sampling rate control method for a multimodal sensing system of the present invention is much better than the existing scheme, and the ST-AoI violation probability is reduced by about 10 times.

[0105] Although the present invention is described by way of specific embodiments, it will be understood by those skilled in the art that various modifications and equivalent substitutions may be made to the present invention without departing from the scope of the present invention. Furthermore, various modifications may be made to the present invention for specific circumstances or materials without departing from the scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed, but is intended to encompass all embodiments falling within the scope of the claims.

[0106] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A sampling rate control method for a multimodal sensing system, characterized in that: include: Multiple sensors continuously send data packets to the receiving device according to their sampling rate; The receiving device calculates an average information age of all sensors in a control cycle according to the received data packets, and determines an update sampling rate of the multiple sensors in a next control cycle based on the pseudo-Jacobian matrix and the average information age; wherein one control period is defined as the receiving end device receiving N data packets from the plurality of sensors, where N is a positive integer; The updated sampling rate in the next control cycle is sent to the multiple sensors respectively, and the multiple sensors continuously send data packets to the receiving end device based on the updated sampling rate in the next control cycle.

2. The sampling rate control method for a multimodal sensing system according to claim 1, wherein: The receiving device calculates an average information age of all sensors in a control cycle according to the received data packets, and determines an update sampling rate of the multiple sensors in a next control cycle based on a pseudo-Jacobian matrix and the average information age, including: Based on the receiving time and generating time of each sensor’s data packet, the average information age of each sensor in a control cycle is calculated; Calculating an optimal solution for the sampling rates of the multiple sensors in a next control cycle based on the average information age, the sampling rate, and the pseudo-Jacobian matrix; An update sampling rate of the plurality of sensors in a next control cycle is determined based on the sampling rate optimal solution and the delay constraint matrix.

3. The sampling rate control method for a multimodal sensing system according to claim 2, wherein: The calculation of the average information age of each sensor within a control cycle based on the reception time and generation time of the data packet of each sensor includes: The average information age of the c-th sensor in the k-th control cycle is calculated based on the following formula: Among them, a c,k represents the average information age of sensor c in the kth control cycle, a c (t) represents the instantaneous information age of sensor c at time t, n c,k represents the number of data packets from sensor c successfully received in the kth control cycle, Y c,k,j represents the system time of the jth data packet of sensor c successfully received in the kth control cycle, X c,k,j represents the time interval between the adjacent data packets of sensor c that are successfully received in the kth control cycle; Y c,k,j-1 The system time of the j-1th data packet of sensor c that is successfully received in the kth control cycle; Indicates the nth sensor c successfully received in the kth control cycle c,k The reception time of a data packet, Indicates the nth sensor c successfully received in the k-1th control cycle c,k-1 The reception time of a data packet.

4. The sampling rate control method for a multimodal sensing system according to claim 3, wherein: The calculating the optimal solution of the sampling rates of the multiple sensors in the next control cycle based on the average information age, the sampling rate, and the pseudo-Jacobian matrix includes: Obtaining an average information age vector sequence of all sensors in the kth control cycle based on the average information age of each sensor; Based on minimizing the average information age violation probability, establishing a mathematical expression between the average information age vector sequence and the sampling rate vector sequence of all sensors; An optimal solution sequence of sampling rates of the multiple sensors in a next control cycle is obtained based on the average information age vector sequence, the pseudo-Jacobian matrix, and the sampling rate vector sequence.

5. The sampling rate control method for a multimodal sensing system according to claim 4, characterized in that: The mathematical expression between the average information age vector sequence and the sampling rate vector sequence of all sensors is: Among them, a k =(a 1,k ,…,a C,k ) T ,u k =(u 1,k ,…,u C,k ) T ,δ=(δ1,…,δ C ) T ;a 1,k represents the average information age of sensor 1 in the kth control cycle, a C,k represents the average information age of sensor C in the kth control cycle, u 1,k represents the sampling rate of sensor 1 in the kth control cycle, u C,k represents the sampling rate of sensor C in the kth control cycle; δ1 represents the average information age threshold of sensor 1, δ represents the average information age threshold vector sequence of all sensors, K represents the number of control cycles, C represents the number of sensors, c∈C, Indicates a violation indicator. is equal to 0 when , and equal to 1 otherwise.

6. The sampling rate control method for a multimodal sensing system according to claim 5, characterized in that: The step of obtaining an optimal solution sequence of sampling rates of the plurality of sensors in a next control cycle based on the average information age vector sequence, the pseudo-Jacobian matrix, and the sampling rate vector sequence includes: The multimodal sensing system is transformed into the following equivalent dynamic linear data model Δa k =V k Δu k ,; where Δu k =u k -u k-1 , Δa k =a k -a k-1 , v k =[v ij,k ] C×c And represents the time-varying C-order pseudo-Jacobian matrix in the k-th control period, whose elements are all bounded quantities and the signs of the elements remain unchanged in different control periods; The estimation formula for the time-varying C-order pseudo-Jacobian matrix is obtained as follows: in, Indicates V k The estimated value of represents the time-varying C-order pseudo-Jacobian matrix V in the k-1th control cycle k-1 The estimated value of; μ represents the weight parameter; Δa k-1 =a k-1 -a k-2 ;Δu k-1 =u k-1 -u k-2 ;a k-1 represents the average information age vector sequence of all sensors in the k-1th control cycle, a k-2 represents the average information age vector sequence of all sensors in the k-2th control cycle; u k-1 represents the sampling rate vector sequence of all sensors in the k-1th control cycle; u k-2 represents the sampling rate vector sequence of all sensors in the k-2th control cycle; Based on the estimated value of the time-varying C-order pseudo-Jacobian matrix The average information age threshold vector sequence δ of all sensors, the sampling rate vector sequence u of all sensors in the k-1th control cycle k-1 , the average information age vector sequence a of all sensors in the k-1th control cycle k-1 Calculate the sampling rate vector sequence u of all sensors in the kth control cycle k As the optimal solution sequence of the sampling rates of the multiple sensors in the next control cycle: in λ represents the weight parameter, And it is the identity matrix.

7. The sampling rate control method for a multimodal sensing system according to claim 6, characterized in that: if or or if Where V0=[v ij,0 ] C×C is the initial time-varying C-order pseudo-Jacobian matrix, θ1, θ2 are positive constants, satisfying the relationship ρ≥1, θ2>θ1(2ρ+1)(C-1).

8. The sampling rate control method for a multimodal sensing system according to claim 6, characterized in that: The step of determining the update sampling rates of the multiple sensors in the next control cycle based on the sampling rate optimal solution and the delay constraint matrix includes: The delay constraint matrix is obtained based on the packet loss rate, the average transmission delay, the second-order moment of the transmission delay, the average information age vector sequence, the pseudo-Jacobian matrix, and the sampling rate vector sequence. when When it is established, the optimal solution sequence u of the sampling rate k As the update sampling rate of the multiple sensors in the next control cycle, otherwise u k =x k [1:C] is the update sampling rate of the multiple sensors in the next control cycle, where: Where min_index represents the index of the sensor with the smallest average information age threshold; λ represents the weight parameter, and is the identity matrix; Indicates V k The estimated value of a k-1 represents the average information age vector sequence of all sensors in the k-1th control cycle, u k-1 represents the sampling rate vector sequence of all sensors of all sensors in the k-1th control cycle, and δ represents the average information age threshold vector sequence of all sensors.

9. The sampling rate control method for a multimodal sensing system according to claim 8, characterized in that: The delay constraint matrix is a symmetric matrix with the main diagonal elements being The remaining off-diagonal elements are They represent the estimated packet loss rate in the kth control cycle, the average transmission delay of N data packets, and the second-order moment of the average transmission delay of N data packets.

10. A sampling rate control system for a multimodal sensing system, comprising a plurality of sensors, a transmitting device and a receiving device, wherein the transmitting device and the receiving device store computer programs for executing the sampling rate control method for a multimodal sensing system according to any one of claims 1 to 9.

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