Industrial electromagnetic interference deterministic modeling and predicting method based on nonlinear regression algorithm

Abstract

The invention relates to an industrial electromagnetic interference deterministic modeling and predicting method based on a nonlinear regression algorithm. The method comprises the following steps: step 1, EMI analysis of industrial equipment and selection of a regression machine learning algorithm; 2, constructing an industrial EMI model based on nonlinear regression, and the like. The method has the technical effects that EMI is simplified into white noise through EM and DM models in a traditional channel modeling method, the modeling precision is limited due to the fact that the EMI is not consistent with the actual characteristics of industrial EMI, and the performance of the EM model is further reduced in application due to lack of environmental pertinence; according to the method, on the premise that persistent additional physical equipment deployment is not needed, historical EMI measurement data and industrial control instruction data generated in normal industrial production are utilized, a complete and accurate industrial EMI deterministic modeling scheme is provided through big data analysis and a machine learning algorithm, implementation is easy, the method is closer to an actual industrial scene, and the method is suitable for popularization and application. Moreover, the method is low in computing resource consumption, and achieves the real-time, efficient, high-precision and complete industrial EMI prediction.

Description

TECHNICAL FIELD

[0001] The present application relates to an industrial electromagnetic interference deterministic modeling and prediction method, and more particularly to an industrial electromagnetic interference deterministic modeling and prediction method based on a nonlinear regression algorithm. BACKGROUND

[0002] 5G newly introduced massive Machine-Type Communication (mMTC) and Ultra-Reliable Low-Latency Communication (URLLC) scenarios significantly expand its application range, especially providing effective communication services for Industrial Internet of Things (IIoT) devices. The continuous iteration of the functions and performance of wireless communication technology makes the vertical industry gradually begin to put wireless communication on the agenda of Operational Technology (OT) network communication on the basis of the previous Information Technology (IT) network's strong embrace of wireless communication. However, for OT networks, the complex and harsh wireless environment in the industrial field, especially the electromagnetic interference (EMI) caused by production equipment and processes in the industrial production process, is a key bottleneck that cannot be avoided in the wireless road.

[0003] By taking advantage of the two characteristics of repeatability and determinacy of industrial production processes, with the help of industrial control information and historical EMI measurement information, and by applying machine learning algorithms, the precise EMI feature information hidden in these two types of information can be mined. Compared with existing statistical-based methods, the method is not only more accurate and has more comprehensive EMI information, but also more suitable for actual wireless communication networks. Similarly, the more accurate and information-rich interference model obtained by using the new EMI modeling scheme also leaves more operating space for resource allocation of OT wireless networks.

[0004] In order to better understand the industrial electromagnetic interference deterministic modeling and prediction method based on a nonlinear regression algorithm proposed in the present patent application, the regression algorithm involved therein is briefly introduced as follows.

[0005] The regression algorithm is a kind of supervised machine learning, which is an algorithm that establishes a model by using existing data and then processes the data to be solved by using this model. The regression algorithm can be expressed in the following general form.

[0006] Known: sample set Wherein, Xi is the independent variable (regressor) of the i-th sample, y (i) is the dependent variable (regressand) of the i-th sample, M is the dimension number of the independent variable, and N is the sample number.

[0007] Assumption: the dependent variable y (i) of the sample is affected by the independent variable x (i) . (i) In addition to the influence of the independent variable x i , there are other quantities that affect y (i) , and there is an error term ∈ (i) independent of the independent variable.

[0008] Model representation: where h(x; θ) is a known function with unknown parameters θ=(θ1, θ2, …, θ K K is the number of unknown parameters, and the solution is as follows:

[0009]

[0010] and the unknown parameters satisfy the constraint condition where ρ(·) is a loss measure function.

[0011] According to the nature of the model established for the regression problem, it is divided into linear regression and nonlinear regression. If h(x; θ) is linear with respect to the independent variable, it is a linear regression problem, otherwise it is a nonlinear regression problem. The constraint condition is optional, and in some problems, there may be no constraint condition, i.e. the unknown parameters can be arbitrarily taken.

[0012] For linear regression problems, there is an analytical solution, i.e. the least squares method; while for nonlinear regression problems, there is no general analytical solution, and iterative algorithms are usually used to solve them.

[0013] In the prior art, EMI is mainly regarded as statistical noise, and channel modeling or statistical methods are used to analyze and model EMI. Traditional channel modeling methods regard EMI as white noise, i.e. directly modeling EMI in the overall modeling of channel characteristics. It can mainly construct two types of models: empirical model (EM) and deterministic model (DM).

[0014] Among them, EM is mainly based on a certain type of wide-ranging scenario (such as the indoor factory InF scenario proposed in the 3GPP standard document), and the wireless channel is measured under different deployment configurations and environments. By fitting the measurement data, one or a group of empirical formulas are obtained to describe the wireless channel.

[0015] On the other hand, DM is mainly targeted at a specific deployment environment. Building a DM requires a fine digital reproduction of the environment first, and the electromagnetic propagation characteristics of various entities in the environment. Based on the digital reproduction of the environment, DM is built by using methods with extremely large amount of computation, such as ray tracing and finite-difference time-domain modeling.

[0016] Unlike traditional channel modeling, the modeling based on statistical methods still regards EMI as noise, but regards it as an independent noise source different from white noise, and performs EMI measurement for a specific deployment environment. Based on the measurement results, two levels of analysis are performed: one is statistical analysis of key performance indicators of wireless communication, such as reference signal received power (RSRP), channel quality indicator (CQI), etc., to quantify the impact of EMI in the current environment on communication quality; the other is statistical modeling of the measured EMI. Existing technologies in the academic field mainly include modeling of statistical characteristics of EMI, such as amplitude probability distribution (APD) and root-mean-square (RMS) delay, and modeling of time-domain or frequency-domain characteristics of EMI.

[0017] On the basis of modeling of EMI, existing technologies also introduce Markov chain algorithm to predict whether EMI pulse will occur at the next moment.

[0018] The EMI and DM models built by traditional channel modeling methods regard EMI as pure white noise, which obviously does not match the characteristics of industrial EMI, so the modeling accuracy of both is quite limited. In addition, the performance of the EM model will also be more significantly degraded when it is applied to a specific environment, because it is not targeted at the characteristics of the specific environment. As for DM, although the model is built completely for a specific environment, it requires very harsh prior environmental information, and the computation amount of the modeling algorithm is extremely large, so it is difficult to be practically applied.

[0019] Although the modeling based on statistical methods no longer regards EMI as white noise, the prior art mainly regards EMI as a purely statistical random process, and thus only performs statistical analysis modeling on EMI. However, the EMI generated by different production equipment and processes is not the same, and thus it is not appropriate to mix all these EMIs together. More importantly, the industrial production process has extremely high repeatability and certainty, and thus only performing statistical EMI modeling cannot fully reflect the characteristics of industrial EMI. Similarly, the EMI prediction using Markov chain can only predict the statistical characteristics of the occurrence of EMI, and cannot give a deterministic prediction result, and thus it still cannot be practically applied in the resource scheduling of industrial OT networks.

[0020] Therefore, the present application proposes an industrial electromagnetic interference deterministic modeling and prediction method based on a nonlinear regression algorithm. Without the need for persistent physical device deployment, the method uses mixed industrial EMI measurement data and control instruction information of each industrial equipment, and through big data analysis and machine learning algorithms, can extract complete and accurate single-equipment-level industrial EMI deterministic models from a large amount of mixed industrial equipment EMI measurement data, and can realize accurate EMI prediction by means of the established models. Without the need for special EMI measurement for a single industrial equipment, the method can construct a unique deterministic interference model for the industrial equipment, and thus is simple to implement and more practical for industrial scenarios. Moreover, the modeling speed is relatively fast, and thus the method can realize efficient, high-precision and complete industrial EMI prediction. SUMMARY

[0021] The present application proposes an industrial electromagnetic interference deterministic modeling and prediction method based on a nonlinear regression algorithm. The method includes two parts of industrial EMI modeling and EMI power prediction. A nonlinear regression algorithm is used to train a prediction model. The input data are historical industrial EMI power measurement data and corresponding collected industrial equipment control instructions, such as a start instruction issued by a programmable logic controller (PLC) to instruct an industrial equipment to start operation, and end information fed back to the PLC after the industrial equipment finishes operation, etc. On the basis of completing modeling, industrial EMI intensity prediction is performed. By inputting the latest industrial equipment control instruction corresponding time stamp of each industrial equipment into the prediction model, the corresponding industrial EMI prediction result can be output.

[0022] The industrial electromagnetic interference deterministic modeling and prediction method based on a nonlinear regression algorithm includes the following steps:

[0023] Step 1. EMI analysis of industrial equipment and selection of regression type machine learning algorithm;

[0024] Step 2. Construction of an industrial EMI model based on nonlinear regression;

[0025] Step 3. Collection, organization and modeling of industrial equipment data;

[0026] Step 4. Model-based EMI power prediction;

[0027] Step 5. Calculation of predicted EMI and noise power

[0028] Further, the EMI analysis of the industrial equipment in Step 1 and the selection of the regression-based machine learning algorithm:

[0029] In an industrial scene, there are Q industrial equipment in the entire scene, some of which are performing production processes, and others are idle. Considering the repeatability and determinacy of the production process, each industrial equipment has a corresponding deterministic EMI emission pattern according to the specific process it performs. For the qth industrial equipment, its EMI pattern at a certain location in the industrial site, at frequency f, at time t is denoted as p q (t,f). The total power of EMI and noise at this location is calculated as shown in equation (1):

[0030]

[0031] where σ 2 is the noise power. The modeling and prediction of industrial EMI are aimed at providing a reference for the planning, deployment, and management of industrial wireless communication. The measurement, modeling, and prediction of industrial EMI for a specific frequency band f0 are required. For the qth industrial equipment, its EMI time-domain pattern at a certain location in the industrial site, at frequency band f0, at time t is denoted as p q (t,f0). The total power of EMI and noise at this location, at frequency band f0, at time t is calculated as shown in equation (2):

[0032]

[0033] According to the measured total power of EMI and noise P(t,f0), the EMI pattern p q (t,f0) of each industrial equipment and the noise power σ 2 of the measurement scene are predicted by a regression-based algorithm. This modeling and prediction is applicable to any EMI equipment deployment scenario.

[0034] Thus, without additional continuous deployment of measurement equipment, the total power of EMI and noise at any time in the industrial wireless communication system under the given industrial equipment working mode (performing process or idle) can be accurately predicted. Regression-based machine learning algorithms are numerous and can be divided into linear regression and nonlinear regression according to the model functions used.

[0035] Based on the total power expression (2) of interference and noise, considering the unpredictability of small-scale fading in the wireless environment, the average power of EMI and noise will be mainly considered, and the small-scale fading will be considered as an error term and not predicted. The error term ε is added to the total power expression (2) of interference and noise, that is, the following formula (3) is obtained:

[0036]

[0037] It is obvious that the above formula (3) is a linear regression model, however, small-scale fading belongs to multiplicative fading, which cannot be captured by additive error terms; at the same time, the EMI power is often small, and directly using linear values for modeling and mining will cause serious numerical precision problems, here, nonlinear regression is introduced as the model function to solve the above problems, as follows:

[0038]

[0039] Wherein, ∈ ′ is an error term, after taking the logarithm of both ends of the equation, the multiplicative small-scale fading becomes additive and can be captured by the error term; in addition, the optimization goal of the algorithm is also changed to the logarithmic value of the sum of system EMI and noise power, which significantly reduces the error caused by numerical precision.

[0040] Further, the construction of the industrial EMI model based on nonlinear regression in step 2:

[0041] Based on the selected nonlinear regression algorithm, the nonlinear model function obtained is as follows:

[0042]

[0043] Wherein, and σ 2 are unknown parameters in the model function, which can be inferred by mining the measurement data set; although the final output value of the model function is in logarithmic form, the internal unknown parameters, i.e. p and σ 2 still present in natural values, resulting in that when constructing the problem, first, the following restriction condition must be added to each unknown parameter:

[0044]

[0045] so that each unknown parameter has its own physical meaning, that is, the power must be positive. After adding the restriction condition, the restriction condition needs to be considered additionally when solving the problem, which not only makes the problem more complex, but also may affect the solving accuracy of each unknown parameter;

[0046] According to the definition of each unknown parameter, its corresponding value is extremely small, as low as 10 -10 In the following, the extremely small numerical value not only needs to use a more complex parameter optimization process when solving the problem, but also causes problems in the precision of computer floating-point number representation. By using the power of each EMI source power and noise as the unknown parameter of the nonlinear model function, the expression is as follows (6):

[0047]

[0048] Wherein,

[0049] Further, the collection, arrangement and modeling of the industrial equipment data in step 3 include:

[0050] Step 3.1 Collection of industrial control instruction data:

[0051] The collection of industrial control instruction data mainly collects two types of industrial control instruction information: one is the start instruction sent by PLC to industrial equipment to indicate the start of action, wherein PLC sends start instruction to certain equipment each time, the corresponding flag bit will be temporarily changed from 0 to 1 and then reset to 0, and each time the flag bit changes, the changed flag bit and the time of change will be recorded, according to the recorded data, the time stamp vector of the start of action of industrial equipment q is obtained as That is, And so on;

[0052] The other is the second type of industrial control data collected by the PLC, which is the end message of the action of the industrial equipment, indicating the completion of the action. According to the data format collected above, the same method as above is used to obtain the time stamp vector of the end of the action of industrial equipment q

[0053] In the collected EMI power measurement data, the time stamp τ of the start of measurement is recorded, then the measurement with serial number 1 is performed, and the measured EMI power is recorded, with every δ seconds as a measurement, the serial number of each measurement is incremented, and N pieces of measured power data are obtained;

[0054] The measured EMI power sequence is denoted as Wherein, And so on;

[0055] For different measurement devices and settings, the measured EMI power unit can be different from the above-mentioned dBW. Other common logarithmic power units include dBμ, dBm, etc. However, as long as the power unit is in logarithmic form, the proposed industrial EMI deterministic modeling and prediction scheme is applicable, and the unit of the unknown parameter mentioned in step 2 will be the same as the measured EMI power value here.

[0056] Step 3.2 Data set preparation of industrial equipment:

[0057] The EMI power measurement interval is fixed as δ seconds. The conversion between the sequence number and the timestamp is carried out by the following formula (6) in seconds:

[0058] t n = τ + δ (n - 1) (6),

[0059] where t n is the timestamp corresponding to the sequence number n, and the industrial control instruction timestamp collected in step 3.1 is converted into the sequence number corresponding to the EMI power data in step 3.2.

[0060] For any specific sequence number n, define as the timestamp in T q that satisfies t < t n and is closest to t n (i.e., represents the time when the industrial equipment q last received a start instruction before the timestamp corresponding to the sequence number n), and define as the timestamp in T te that satisfies t q < t and is closest to t 2 (i.e., the end message timestamp corresponding to the action after the start instruction received by the industrial equipment q at t is executed), and using formula (6), convert and to corresponding sequence numbers and

[0061] Introduce the following formula (7) to indicate the sequence number offset of the industrial equipment q since the last action is executed at sequence number n:

[0062]

[0063] This variable also indicates whether the industrial equipment is executing an action (i.e., generating EMI): if , it means that the industrial equipment q is in an idle state at sequence number n and does not generate EMI;

[0064] Finally, sequence number n and the offset and the measured EMI power information are put together, i.e. the final data set is obtained;

[0065] Step 3.3 EMI modeling of industrial equipment:

[0066] Based on the obtained nonlinear model function Meanwhile, the conversion between time and serial number is performed by using the above formula (6), and the actual used objective function is formula (8) as follows:

[0067]

[0068] wherein,

[0069] The final data set obtained by using step 3.2 is used to solve the following formula (9) unconstrained nonlinear least square (UNLS) problem:

[0070]

[0071] That is, the EMI model and noise power of each industrial equipment are obtained, and the aforementioned UNLS problem is solved by using iterative algorithms such as trust region, and the unknown parameter value which can make the sum of the prediction squared deviations of each data in the data set minimum is obtained as the solution of the problem, denoted as and

[0072] Further, the EMI power prediction based on the model in step 4 is:

[0073] The EMI model of each industrial equipment is obtained by completing the modeling in step 3 and the noise power Then, the EMI model of each industrial equipment is used and the noise power and the EMI power at the moment is predicted in combination with the industrial control instruction.

[0074] Further, the predicted EMI and noise power in step 5 is calculated:

[0075] The EMI model of each industrial equipment and the serial number offset are substituted into the following formula (10), i.e. the predicted EMI and noise power corresponding to the to-be-solved moment

[0076]

[0077] Further, in step 4, the EMI power at the moment is predicted, including the following steps:

[0078] Step 4.1 converting the time stamp into serial number, denoting the time to be predicted EMI as Industrial equipment q in Before the time The last start instruction received from the PLC corresponds to a timestamp And the timestamp of the feedback end message corresponding to the start instruction is Apply formula (6), that is, convert the aforementioned three timestamps into serial numbers And Here, in view of the subsequent focus on And The τ in formula (6) can be arbitrarily specified here, as long as the value of τ remains consistent when converting the three timestamps, if the action at Time has not been completed (i.e. Does not exist), then Obviously, its converted serial number

[0079] Step 4.2 serial number mapping, serial number Mapping to the serial number offset corresponding to each industrial equipment using the above formula (6)

[0080] Compared with the prior art in the technical field, the present application has the following superior technical effects:

[0081] 1. The EM and DM models in the traditional channel modeling method simplify EMI as white noise, which does not conform to the actual characteristics of industrial EMI, resulting in limited modeling accuracy. The EM model further deteriorates in performance in specific applications due to the lack of environmental specificity. The DM model, although specific to a particular environment, relies on a large amount of prior information and is computationally complex, making it difficult to use. The statistical modeling method no longer assumes that EMI is white noise, but still analyzes it as a random process, ignoring the differences in EMI generated by different equipment and processes, and also failing to reflect the high degree of determinism and repeatability in industrial production. Therefore, even if statistical prediction methods such as Markov chains are used, only statistical descriptions can be provided rather than deterministic predictions, which cannot effectively support resource scheduling applications for industrial OT networks; the industrial electromagnetic interference deterministic modeling and prediction method based on the nonlinear regression algorithm described in the present application does not require the deployment of persistent additional physical equipment, but uses historical

[0082] EMI measurement data and industrial control instruction data generated in normal industrial production through big data analysis and machine learning algorithms to provide a complete and accurate industrial EMI deterministic modeling scheme, which is simple to implement, closer to the actual industrial scene, and consumes less computing resources, achieving real-time, efficient, high-precision, and complete industrial EMI prediction.

[0083] 2.The industrial electromagnetic interference (EMI) deterministic modeling and prediction method based on the nonlinear regression algorithm, without the need for persistent additional deployment of physical devices, but due to the full consideration of the industrial EMI determinacy, the precise positioning of EMI is realized with the help of industrial control instruction information, and the model function based on the nonlinear regression, and the EMI model power expression method of each industrial device expressed in logarithmic units, so that the problem modeling of the algorithm is more suitable for the causes and composition of industrial EMI, and the unknown parameters (i.e., the EMI model power of each industrial device expressed in dBW and the noise power) are also more suitable for the problem of modeling, thus greatly reducing the prediction error of the algorithm, and can be actually used in industrial wireless networks.

[0084] 3.For the problem that the existing industrial EMI prediction relies on a probability statistical model, resulting in low accuracy and non-reproducible results, the key point of the industrial electromagnetic interference (EMI) deterministic modeling and prediction method based on the nonlinear regression algorithm is to embed the highly deterministic characteristics of the EMI of the industrial device in the operation process into the nonlinear regression loss function as a prior constraint, and to locate the start and end time of each EMI emission of each industrial device by using the industrial control instruction information, so that under the condition that the EMI emitted by each industrial device does not need to be measured separately, only relying on the measured mixed EMI data containing a large number of device emissions, an accurate time-domain EMI model of each industrial device can be constructed, replacing the traditional probability distribution fitting scheme.

[0085] 4.On the basis of completing the EMI modeling, the EMI power prediction method based on the nonlinear regression algorithm of the present application is proposed, which converts the to-be-predicted time point and the industrial control instruction data closest to the to-be-predicted time point into a serial number offset to input the prediction model, and can output the corresponding EMI power prediction result in real time. BRIEF DESCRIPTION OF DRAWINGS

[0086] Figure 1 It is a typical industrial field scene diagram of the present application;

[0087] Figure 2 It is an EMI power prediction flowchart of the present application;

[0088] Figure 3 It is a whole flowchart of the user-to-user uplink interference modeling and prediction scheme based on the nonlinear regression algorithm of the present application;

[0089] Figure 4 It is a practical measurement and performance evaluation scene diagram of the present application;

[0090] Figure 5 It is the measured value of the EMI power and the prediction value of each scheme of the present application;

[0091] Figure 6 For the whole D te Prediction absolute error CDF of each scheme for the data points affected by EMI of the present application

[0092] Figure 7 Prediction absolute error CDF of each scheme for the data points affected by EMI of the present application DETAILED DESCRIPTION

[0093] In order to clearly understand the technical solutions of the industrial electromagnetic interference deterministic modeling and prediction method based on a nonlinear regression algorithm provided by the present application, the specific embodiments of the present application are described in detail below in combination with the accompanying drawings of the specification.

[0094] The present application provides an industrial electromagnetic interference deterministic modeling and prediction method based on a nonlinear regression algorithm, which includes two parts of industrial EMI modeling and EMI power prediction. The nonlinear regression algorithm is used to train the prediction model. The input data is the historical industrial EMI power measurement data and the corresponding collected industrial equipment control instructions, such as the start-up instructions of the programmable logic controller (PLC) issued to indicate the industrial equipment to start operation, and the end information fed back to the PLC after the industrial equipment operation, etc. On the basis of completing the modeling, the industrial EMI intensity prediction is carried out. The latest industrial equipment control instruction time stamp of each industrial equipment is input into the prediction model, which can output the corresponding industrial EMI prediction result.

[0095] The industrial electromagnetic interference deterministic modeling and prediction method based on a nonlinear regression algorithm includes the following steps:

[0096] Step 1. EMI analysis of industrial equipment and selection of regression type machine learning algorithm

[0097] As shown in Figure 1 In the industrial scene, there are Q industrial equipment in the whole scene, and part of the stations are executing production procedures, and the other stations are in idle state. Considering the repeatability and certainty of the production procedure, each industrial equipment will have a corresponding deterministic EMI emission mode according to the specific procedure it executes. For the qth industrial equipment, the mode of EMI at t time in a position of the industrial field and f frequency point can be recorded as p q (t,f). The total power of EMI and noise at the position is calculated as shown in the following formula (1):

[0098]

[0099] Where, σ 2is the noise power. The modeling and prediction of industrial EMI, which aims to provide reference basis for the planning, deployment and management of industrial wireless communication, needs to measure, model and predict the industrial EMI of a specific frequency band f0. For the qth industrial device, the EMI time-domain mode corresponding to a position in the industrial field, a frequency band f0 and a time t is denoted as p q (t,f0). The total power of EMI and noise at time t in the position and frequency band f0 is as follows (2):

[0100]

[0101] According to the measured total power data P(t,f0) of EMI and noise, i.e. by using a regression algorithm to predict the EMI mode p q (t,f0) of each industrial device and the noise power σ 2 in the measurement scene, the modeling and prediction here are also applicable to any EMI device deployment scene;

[0102] Thus, without additional continuous deployment of measurement devices, the total power of EMI and noise at any time under the given industrial device working mode (executing a process or idle) can be accurately predicted. There are numerous regression machine learning algorithms, which are divided into linear regression and nonlinear regression according to the model functions used;

[0103] Based on the total power expression (2) of interference and noise, considering the unpredictability of small-scale fading in the wireless environment, the average power of EMI and noise will be mainly considered, and small-scale fading will be regarded as an error term and not predicted. An error term ∈ is added to the total power expression (2) of interference and noise, i.e. the following formula (3) is obtained:

[0104]

[0105] It is obvious that the above formula (3) is a linear regression model. However, small-scale fading belongs to multiplicative fading and cannot be captured by additive error terms. At the same time, EMI power is often small, and directly using linear values for modeling and mining will cause serious numerical precision problems. Here, nonlinear regression is introduced as the model function to solve the above problems, as follows (4):

[0106]

[0107] wherein, ∈ ′ is an error term. After taking the logarithm of both sides of the equation, the multiplicative small-scale fading becomes additive and can be captured by the error term. In addition, the optimization objective of the algorithm is changed to the logarithmic value of the sum of system EMI and noise power, which significantly reduces the error caused by numerical precision;

[0108] Step 2. Construction of industrial EMI model based on nonlinear regression

[0109] Based on the selected nonlinear regression algorithm, the obtained nonlinear model function is as follows (5):

[0110]

[0111] wherein, and σ 2 are unknown parameters in the model function, which can be inferred by the nonlinear regression algorithm by mining the measurement data set; although the final output value of the model function is in logarithmic form, the internal unknown parameters, i.e. p and σ 2 still present in natural values, resulting in that when constructing the problem, first, the following constraint condition needs to be added to each unknown parameter:

[0112]

[0113] in order to make each unknown parameter have its own physical meaning, i.e. the power must be positive, after adding the constraint condition, the constraint condition needs to be considered additionally when solving the problem, which not only makes the problem become complex, but also affects the solving accuracy of each unknown parameter;

[0114] Secondly, according to the definition of each unknown parameter, the corresponding value is extremely small, as low as 10-10 or below, the extremely small value not only makes the parameter optimization complex in the solving algorithm level, but also the too small value may cause problems in the computer floating-point number representation precision, by using the power of each EMI source power and noise as the unknown parameter of the nonlinear model function, the expression is as follows (6):

[0115]

[0116] wherein,

[0117] Step 3. Collection, arrangement and modeling of industrial equipment data

[0118] Step 3.1 Collection of industrial control instruction data:

[0119] The collection of industrial control instruction data mainly collects two types of industrial control instruction information: one is the start instruction sent by the PLC to the industrial equipment to instruct it to start action, as shown in the following table 1:

[0120] Table 1

[0121] Flag bit Timestamp 1 15:19:04.93 0 15:19:05.29 1 15:20:27.93 0 15:20:28.79 … … 1 17:28:16.33 0 17:28:16.67

[0122] Wherein, PLC sends start instruction to a device each time, its corresponding flag bit will be temporarily changed from 0 to 1, and then reset to 0, each time the flag bit changes, the embodiment records the changed flag bit and the time stamp as shown in Table 1, according to the recorded data, the time stamp vector of the start of the action of the industrial equipment q is arranged as Taking Table 1 as an example, that is, And so on.

[0123] And the second type of industrial control data collected is the end message of the action execution of the industrial equipment feedback to the PLC, the corresponding collected data format is the same as Table 1, and the time stamp vector of the end of the action of the industrial equipment q can also be arranged in the same way as described above

[0124] In the embodiment, the collected EMI power measurement data is in the form shown in Table 2, wherein the time stamp τ of the start of the measurement is recorded, then the measurement with the serial number 1 is performed, and the measured EMI power is recorded, and the measurement is performed every δ seconds, the serial number of each measurement is incremented, and N pieces of measured power data are obtained.

[0125] Table 2

[0126] Start time τ 15:21:40.21 Serial number n EMI power (dBW) 1 -117.28 2 -116.82 … … 7842 -111.59 7843 -113.16 … … N-1 -116.87 N -116.67

[0127] Up to now, the EMI power sequence measured in the embodiment is denoted as Wherein, And so on.

[0128] It should be noted that different measurement equipment and settings may result in different units of the measured EMI power from the above-mentioned dBW, other common logarithmic power units include dBμ, dBm, etc., but as long as the power unit is in logarithmic form, the proposed industrial EMI deterministic modeling and prediction scheme can be normally applied, and the unit of the unknown parameter mentioned in step 2 will also be the same as the measured EMI power value;

[0129] Step 3.2 Data set arrangement of industrial equipment:

[0130] In this example, the EMI power measurement interval is fixed at δ seconds, and the conversion between the serial number and the time stamp is performed by the following formula in seconds, as shown in the following formula (6):

[0131] t n = τ + δ (n-1) (6),

[0132] Wherein, t nThe timestamps of the industrial control commands collected in step 3.1 are converted to the sequence number corresponding to the EMI power data in step 3.1 for the timestamp corresponding to sequence number n;

[0133] For any specific sequence number n, define For T q The timestamp t that satisfies t < t and is closest to t (i.e., represents the time when the industrial device q last received a start command before the timestamp corresponding to sequence number n), and define For The timestamp t that satisfies t < t and is closest to t (i.e., represents the time when the industrial device q last received a start command before the timestamp corresponding to sequence number n), and define For The timestamp t that satisfies t < t and is closest to t (i.e., represents the time when the industrial device q last received a start command before the timestamp corresponding to sequence number n), and define For And are converted to the corresponding sequence numbers And

[0134] The following variable shown in equation (7) is introduced to indicate the sequence number offset of the industrial device q since the last action started at sequence number n:

[0135]

[0136] This variable also indicates whether the industrial device is performing an action (i.e., generating EMI): if It means that the industrial device q is in an idle state at sequence number n, and no EMI is generated.

[0137] Finally, the sequence number n, the offset of each industrial device, and the measured EMI power information are sorted, and the final data set as shown in Table 3 is obtained.

[0138] Table 3

[0139]

[0140] Step 3.3 Industrial device EMI modeling:

[0141] Based on the obtained nonlinear model function And using the above equation (6) to convert between time and sequence number, the target function actually used in this embodiment is obtained, as shown in equation (8):

[0142]

[0143] Wherein,

[0144] Using the final data set obtained in step 3.2, solve the following equation (9) of unconstrained nonlinear least squares (UNLS):

[0145]

[0146] That is, the EMI model and noise power of each industrial equipment are obtained, and the aforementioned UNLS problem is solved by using an iterative algorithm such as a trust region, and the value of the unknown parameter that can minimize the sum of the prediction squared deviations of each data in the data set is obtained as the solution to the problem, denoted as

[0147] Step 4 Model-based EMI power prediction

[0148] The EMI model of each industrial equipment is obtained by completing the modeling in step 3 and the noise power After that, the EMI model of each industrial equipment and the noise power are used to predict the EMI power in real time in combination with the industrial control instructions;

[0149] Step 5 Calculation of predicted EMI and noise power

[0150] Substitute the EMI model of each industrial equipment and the sequence number offset into the following equation (10), which is the predicted EMI and noise power corresponding to the to-be-solved time

[0151]

[0152] Specifically, as shown in Figure 2 , in step 4, the EMI power in real time is predicted, including the following steps:

[0153] Step 4.1 Convert the time stamp into a sequence number, and denote the time to be predicted EMI as , the time when the industrial equipment q receives the last start instruction from the PLC before is The time stamp corresponding to the start instruction is , and the time stamp of the feedback end message corresponding to the start instruction is Apply the above equation (6), and the aforementioned three time stamps can be converted into sequence numbers and Here, since subsequent attention is mainly paid to the relative difference between and , τ in equation (6) can be arbitrarily specified here, as long as the value of τ remains the same when converting the three time stamps. If the action has not been completed at the time (that is, If not, let Obviously, the converted sequence number

[0154] Step 4.2 performs sequence number mapping, and converts the sequence number The sequence number offset corresponding to each industrial equipment is mapped using the above formula (6)

[0155] It should be noted that the industrial electromagnetic interference modeling and prediction scheme based on the nonlinear regression algorithm of the present application is different from the traditional method of statistical EMI analysis and modeling based on historical data. The present application utilizes the historical measurement data of industrial EMI and combines the collected industrial control instructions to complete the deterministic and accurate modeling of each industrial equipment EMI.

[0156] First, the collected data is cleaned, and the data items during the long-term downtime of the production line and the long-term idle period of the industrial equipment caused by maintenance and troubleshooting are appropriately excluded, and then the data is arranged into a training data set (step 1); according to the arranged training data set, the deterministic and accurate modeling of the industrial equipment EMI can be performed (step 2); after the modeling is completed, the industrial equipment EMI model is obtained (step 3).

[0157] The above steps 1-3 are the overall process of industrial equipment EMI modeling. After obtaining the complete industrial EMI model, the model is used to specify the prediction time point, and the industrial control instructions of each industrial equipment near the prediction time point that meet the conditions are input, which are converted into offset and substituted into the EMI power prediction function (step 4), and the EMI+noise power prediction value can be calculated and output (step 5).

[0158] It should be noted that after the industrial equipment EMI modeling is completed, the industrial EMI model obtained in step 3 can be used not only for the EMI power prediction part (i.e. subsequent steps 4-5). Since EMI is a core problem that is extremely prominent in industrial field wireless networks, in fact, the interference model obtained in this step has broad application prospects, and in wireless resource management alone, the following practical applications can be obtained:

[0159] By directly applying the EMI model, the serious defects of existing inter-cell interference coordination (ICIC), enhanced ICIC (eICIC), etc. that do not consider industrial EMI are compensated;

[0160] By using the interference model in the online prediction part of the present application, the EMI power prediction value output in step 5 is used to assist subsequent wireless resource scheduling and allocation.

[0161] The performance of the proposed REPA scheme is introduced from the perspectives of qualitative analysis and quantitative analysis, respectively.

[0162] Comparison scheme selection:

[0163] In this embodiment, the statistical EMI modeling scheme based on continuous hidden Markov model proposed in document 1 [Ze, Y., Liu, L., Cheng, T., Kun, Z., & Jianhua, Z. (2019). Measurement Based Characterization of Electromagnetic Noise for Industrial Internet of Things at Typical Frequency Bands. 2019 IEEE Wireless Communications and Networking Conference (WCNC), 1-6. https: / / doi.org / 10.1109 / WCNC.2019.8885603 (Continuous Hidden Markov Model, CHMM)] (hereinafter referred to as the “comparison scheme” or simply “Ref”) is used as a comparison to demonstrate the superior performance of the nonlinear regression scheme proposed in the present application compared to the closest and most optimal existing scheme. In particular, since the comparison scheme produces a hidden state sequence rather than directly predicting EMI power, the hidden state sequence is converted into EMI power using two commonly used methods, and then compared with REPA:

[0164] Ref-AVG: The mean value of the emission distribution corresponding to each hidden state is taken as the prediction corresponding to the state

[0165] EMI power;

[0166] Ref-SPL: Random sampling is performed according to the emission distribution corresponding to each hidden state in the sequence, and the sampled value is taken as the predicted EMI power corresponding to the state.

[0167] EMI measurement scenarios and dataset characteristics:

[0168] In this embodiment, the data obtained by measuring and collecting instructions at two workstations in a welding workshop of a new energy vehicle factory are used for subsequent performance evaluation, as shown in FIG. 1. Figure 4 As shown in FIG. 1, the industrial equipment in workstation 1 is an arc welding machine, and the industrial equipment in workstation 2 is a stud welding machine. Both of them can produce obvious EMI at the measured frequency points when performing welding actions. Obviously, in this scenario, Q = 2.

[0169] Table 4 below summarizes the parameters used in the measurement.

[0170] Table 4

[0171] Parameter Value measurement frequency point f0 6.8337 MHz Measurement interval δ 10 ms Resolution bandwidth (RBW) 100 kHz Video bandwidth (VBW) 10 kHz Attenuation 0 dB Pre-amplifier Off

[0172] During the measurement, after cleaning, a total of 117,005 data points were collected. Following the method shown in step 3, the collected data was organized into a dataset. The training dataset D... tr Contains N tr = 32,001 data points, and the remaining N te =All 85004 data points were included in the test dataset D te ;

[0173] In D tr In the middle, a total of 1790 data points (accounting for 5.59%) were affected by EMI from industrial equipment; while in D te Of the 5461 data points (5.37%), a total of 5461 were affected. This shows that the characteristics of the two datasets are very similar.

[0174] Qualitative analysis

[0175] Depend on Figure 5 The differences in predicted performance between the various solutions are clearly visible. It can be seen that the predicted EMI from REPA is very close to the measured values ​​(e.g., Figure 5 (As shown in the upper left corner), conversely, the EMI prediction values ​​generated by Ref-AVG and Ref-SPL differ significantly from the measured values. Ref-AVG and Ref-SPL often predict the presence of EMI even when no EMI is measured. Figure 5 (Top right corner) Or, if EMI cannot be predicted at data points where it is actually present, it is clear that the accuracy and recall of Ref-AVG and Ref-SPL predictions are both poor. The reason for this is that REPA directly considers the determinism of industrial EMI during prediction, while Ref-AVG and Ref-SPL rely solely on the statistical characteristics of EMI for prediction. Therefore, Ref-AVG and Ref-SPL lack accuracy in the time-domain precise prediction, which is more important in practical applications.

[0176] Quantitative analysis

[0177] The significant differences found in the qualitative analysis between REPA and the control protocol will be analyzed quantitatively from multiple perspectives in this section:

[0178] 1. Overall performance of prediction

[0179] The root-mean-square error (RMSE) is used here:

[0180]

[0181] The overall performance (dBW) of EMI prediction for each scheme is measured by the RMSE values under different statistical range types, as shown in Table 5.

[0182] Table 5

[0183]

[0184] The overall performance (dBW) of EMI prediction for each scheme is measured by the RMSE values under different statistical range types, as shown in Table 5. te When performing EMI prediction, REPA can achieve a prediction RMSE of 0.4357 dBW. For the data points affected by EMI, which are more concerned in practical applications, the prediction RMSE is only 1.1207 dBW. Such performance is accurate enough for practical applications, because the RMSE is usually smaller than the CQI required to determine the Modulation and Coding Scheme (MCS), and the difference between the corresponding Signal-to-Interference Ratio (SINR) thresholds of adjacent levels.

[0185] Considering each EMI source, for the data points affected by EMI in station 1, the prediction RMSE is 1.2033 dBW; and for the data points affected by EMI in station 2, the prediction RMSE is 0.6403 dBW, which are different. The main reason may be due to the difference in waveform characteristics. For EMI in station 1, each pulse has a longer duration and larger fluctuation, resulting in an increased prediction error. For EMI in station 2, the shorter pulse duration makes the fluctuation less influential. In addition, since the test set is also measured data, it also contains channel fading and other factors that cannot be excluded, so the RMSE value obtained in this embodiment may be larger.

[0186] However, the overall RMSE of Ref-AVG and Ref-SPL exceeds 1.3 dBW, and the prediction RMSE of the data points containing EMI is close to 4 dBW. Such a significant difference in prediction performance reflects the huge impact of Ref-AVG and Ref-SPL being able to only perform statistical modeling and being unable to align in the time domain.

[0187] 2. Cumulative distribution and key quantile values of prediction error

[0188] With the help of Cumulative Distribution Function (CDF), the prediction error of each data point in the data set can be seen more specifically. In order to achieve this purpose better, the absolute error is used here:

[0189]

[0190] The prediction error is measured, and the entire test data set D te The CDF (dBW) of the prediction absolute error is shown in Figure 6 Since the data set is mainly composed of data points not affected by EMI, the measured data of this part is relatively stable. The three curves in the figure do not have a big gap on the left side, and this phenomenon is further confirmed in Table 6, that is, the difference between the median of the prediction absolute error of the three is less than 0.12 dBW.

[0191] Table 6

[0192]

[0193] However, for the data points affected by EMI, the volatility is large; and the superposition of the comparative scheme cannot accurately predict EMI in the time domain, resulting in the two curves corresponding to the comparative scheme showing long and fat tails on the right side of the result graph, so for Ref-AVG and Ref-SPL, the 99th percentile of the absolute error is very large: for Ref-AVG, the value exceeds 5 dBW, and for Ref-SPL, it is close to 6 dBW.

[0194] Considering the data points affected by EMI, in Figure 7 , it is very obvious to see the performance gap between REPA and the comparative scheme. According to the data shown in Table 8 on the prediction performance of the comparative scheme on the occurrence of EMI, the false negative rate of the comparative scheme reaches 98.34%, indicating that in its prediction, most of the data points affected by EMI actually do not exist significant EMI, and since the difference between the prediction values given by Ref-AVG and Ref-SPL is negligible compared to the power difference caused by EMI, in Figure 7 , the curves corresponding to the two are very close.

[0195] Table 7

[0196]

[0197] With a very high false negative rate (98.34%) and an absolute error 99th percentile of more than 7 dBW, as shown in Table 7, it is clear that the comparative scheme cannot meet the demand of accurate time-domain prediction. However, among the prediction sequence generated by the comparative scheme, 4.84% of the data points are predicted to be affected by EMI, which is close to the proportion of data points affected by EMI in the training data set (5.59%). This shows that the comparative scheme is indeed in operation, and the prediction sequence it generates has similar statistical characteristics to the training data set, rather than point-to-point accurate time-domain prediction.

[0198] Table 8

[0199]

[0200] On the contrary, REPA can achieve an absolute error 99th percentile of less than 3 dBW, showing its superior prediction accuracy. The huge performance gap highlights the need for EMI time-domain alignment with additional information (such as industrial control instruction information) during prediction.

[0201] The above disclosure is only one preferred embodiment of the present application, and obviously cannot limit the protection scope of the present application with the specific embodiments provided by the present application. Various changes and improvements made in accordance with the present application without departing from the concept and scope of the present application still belong to the protection scope covered by the claims of the present application.

Claims

1. A method for industrial EMI deterministic modeling and prediction based on nonlinear regression algorithm, comprising the following steps: Step 1. EMI analysis of industrial equipment and selection of regression-based machine learning algorithm; Step 2. Construction of industrial EMI model based on nonlinear regression; Step 3. Collection, organization and modeling of industrial equipment data; Step 4. EMI power prediction based on model; Step 5. Calculation of predicted EMI and noise power.

2. The method for deterministic modeling and prediction of industrial electromagnetic interference based on nonlinear regression algorithm as claimed in claim 1, wherein, Step 1. EMI analysis of industrial equipment and selection of regression-based machine learning algorithm: In an industrial scene, there are Q industrial devices in total in the scene, some of which are performing production processes, and others are in an idle state. Considering the repeatability and certainty of the production processes, each industrial device will have a corresponding deterministic EMI emission pattern according to the specific process it performs. For the qth industrial device, the pattern of EMI at a certain location in the industrial site at f frequency at t time can be denoted as p q (t,f). The total power of EMI and noise at this location is calculated as shown in the following formula (1): where σ 2 Modeling and prediction of industrial EMI, aiming to provide reference for planning, deployment and management of industrial wireless communication, need to measure, model and predict the industrial EMI of a specific frequency band f0. For the qth industrial device, the EMI time-domain mode corresponding to a position in the industrial field, a frequency band f0 and time t is denoted as p q (t, f0). The total power of EMI and noise at the position, frequency band f0 and time t is as follows (2): From the above equation (2), the EMI pattern p(t,f0) of each industrial equipment is predicted from the measured total power data P(t,f0) of EMI and noise, i.e. by a regression-based algorithm q (t,f0) and the noise power σ 2 in the measurement scenario, where the modeling and prediction are equally applicable to any EMI equipment deployment scenario; Thus, without additional continuous deployment of measurement equipment, the total power of EMI and noise at any time of the entire industrial wireless communication system under the given industrial equipment working mode can be accurately predicted, and the number of regression-based machine learning algorithms is large, which can be divided into linear regression and nonlinear regression according to the model function used; Based on the total power expression (2) of interference and noise, considering the unpredictability of small-scale fading in the wireless environment, the average power of EMI and noise will be mainly considered, and the small-scale fading will be regarded as an error term and not predicted. Add error term ε to the total power expression (2) of interference and noise, that is, the following formula (3): The above formula (3) is a linear regression model, while small-scale fading belongs to multiplicative fading and cannot be captured by additive error terms. At the same time, the EMI power is small, and direct modeling and mining with linear values will cause significant numerical precision problems. Therefore, nonlinear regression is introduced as the model function, as shown in the following formula (4): where, is the error term, the multiplicative small-scale fading becomes additive after taking the logarithm of both sides, and is captured by the error term; in addition, the optimization objective of the algorithm becomes the log of the sum of the system EMI and the noise power, reducing the error caused by numerical precision.

3. The method for deterministic modeling and prediction of industrial electromagnetic interference based on nonlinear regression algorithm as claimed in claim 1, wherein, Step 2. Construction of industrial EMI model based on nonlinear regression: Based on the selected nonlinear regression algorithm, the nonlinear model function obtained is as follows (5): where, and σ 2 are unknown parameters in the model function, which can be estimated by mining the measurement dataset; although the final output of the model function is in logarithmic form, the internal unknown parameters, i.e. p and σ 2 still present in natural values, resulting in the need to add the following constraints to each unknown parameter when constructing the nonlinear regression problem: So that each unknown parameter has its own physical meaning; According to the definition of each unknown parameter, its corresponding value is as low as 10 -10 In the following, the extremely small value not only needs to use a more complex parameter optimization process when solving the problem, but also causes problems in the precision of computer floating-point number representation. By using the power of each EMI source power and noise as the unknown parameter of the nonlinear model function, the expression is as follows (6): wherein 4. The method for deterministic modeling and prediction of industrial electromagnetic interference based on nonlinear regression algorithm as claimed in claim 1, wherein, Step 3. Collection, organization and modeling of industrial equipment data, including: Step 3.1 Collection of industrial control command data: The collection of industrial control instruction data mainly collects two types of industrial control instruction information: one is the start instruction sent by the PLC to the industrial equipment to instruct it to start action, wherein the PLC sends the start instruction to the equipment each time, the corresponding flag bit will be temporarily changed from 0 to 1 and then reset to 0, and each time the flag bit changes, the changed flag bit and the time stamp of the change are recorded, and according to the recorded data, the time stamp vector of the start of the action of the industrial equipment q is obtained as q∈[1,Q], that is, and so on. Another is the second type of industrial control data collected for the industrial equipment feedback to the PLC, indicating the end of the action to perform the message, the corresponding data format collected, the same method as described above to obtain the time stamp vector of the end of the action of the industrial equipment q q∈[1,Q] In the collected EMI power measurement data, the time stamp τ at the start of measurement is recorded, then the measurement with serial number 1 is performed, and the measured EMI power is recorded. The measurement is performed every δ seconds, and the serial number is incremented each time, a total of N measured power data; Let the measured EMI power sequence be denoted as wherein, and so on. For different measurement equipment and settings, the measured EMI power unit will be different from the above dBW. Other common logarithmic power units include dBμ and dBm. As long as the power unit is in logarithmic form, the proposed industrial equipment EMI deterministic modeling and prediction scheme is still applicable, and the unit of the unknown parameter mentioned in step 2 will be the same as the measured EMI power value here; Step 3.2 Organization of industrial equipment data set: The EMI power measurement interval is fixed at δ seconds. The conversion between serial number and time stamp is performed by the following formula (6) in seconds: t n = τ + δ(n - 1) (6), where t n convert the industrial control command timestamp collected in step 3.1 into the sequence number corresponding to the EMI power data in step For any specific index n, define For T q In the middle, satisfy t <t n And with t n The nearest timestamp represents the time when industrial device q last received a start command before the timestamp corresponding to sequence number n, and is defined as follows: for China satisfies And with The closest timestamp, that is, the industrial equipment q at After the start command received at the time begins to execute the action, the timestamp of the end message corresponding to this action is used to calculate the time using equation (6). and Convert them to their corresponding serial numbers respectively and The variable shown in the following formula (7) is introduced to indicate the serial number offset of industrial equipment q since its last action at serial number n: The variable also has the role of indicating whether the industrial device is performing an action: if then it means that the industrial device q is in an idle state at the instant n and does not generate EMI; Finally, the serial number n, the offset corresponding to each industrial equipment and the measured EMI power information are arranged together, i.e. the final dataset is obtained; Step 3.3 Industrial equipment EMI modeling: Based on the obtained nonlinear model function At the same time, the conversion between time and serial number is carried out by using the above formula (6), and the target function actually used is obtained as the following formula (8): wherein Using the final data set obtained by step 3.2, solve the following formula (9) unconstrained nonlinear least squares UNLS problem: The EMI model and noise power of each industrial equipment are obtained, and the UNLS problem is solved by using iterative algorithm such as trust region, and the unknown parameter value which can minimize the sum of prediction square deviation of each data in the data set is taken as the solution of the problem, denoted as and 5. The method for deterministic modeling and prediction of industrial electromagnetic interference based on nonlinear regression algorithm as claimed in claim 1, wherein, Step 4 Model-based EMI power prediction: The EMI model of each industrial device is obtained by completing modeling in step 3 and noise power Then, the EMI model of each industrial device is used to predict the EMI power in real time and noise power in combination with the industrial control instructions.

6. The method for deterministic modeling and prediction of industrial electromagnetic interference based on nonlinear regression algorithm as claimed in claim 1, wherein, Step 5 Calculation of predicted EMI and noise power: Substitute the EMI model and the serial number offset of each industrial equipment into the following formula (10), and the predicted EMI and noise power corresponding to the time to be solved is obtained 7. The method for deterministic modeling and prediction of industrial electromagnetic interference based on nonlinear regression algorithm as claimed in claim 1, wherein In Step 4, the EMI power is predicted on-the-fly, including: Step 4.1 Convert timestamps to sequence numbers, let the time to predict EMI be Industrial equipment q is in Before the time The last start instruction received from the PLC corresponds to a timestamp And the timestamp of the feedback end message corresponding to the start instruction is Apply the above formula (6) to convert the aforementioned three timestamps into sequence numbers And Here, given that subsequent attention is mainly focused on the relative difference between And In formula (6), τ is arbitrarily specified here, as long as the value of τ remains consistent when converting the three timestamps, if the action at Time has not been completed, that is Does not exist, then Obviously, its converted sequence number Step 4.2 performs sequence number mapping, mapping the sequence number The sequence number offset corresponding to each industrial device is used for mapping the above formula (6) to

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