The Industrial Internet of Things (IIoT) is of strategic importance in the new era of industrial big data, creating a brand-new industrial ecosystem. Considering the unknown parameters in the IIoT-based industrial process control systems, this paper combines the artificial fish swarm algorithm (AFSA) and the particle filtering (PF) algorithm into the AFSA-PF algorithm based on the self-organizing state space (SOSS) model. The AFSA-PF algorithm not only can estimates the system state but also can make the sampling distribution of the unknown parameter to move the true parameter distribution. Ultimately, the true values of the unknown parameters are identified. In this way, the system model can gradually approximate the actual IIoT-based industrial process control system.

The Internet of Things (IoT) has entered various areas of our lives, such as smart light bulbs and shared bikes to smart locks [

Coupled with emerging information technologies (ITs) such as cloud computing and big data, the IoT evolves into the industrial IoT (IIoT). The IIoT is of strategic importance in the new era of industrial big data, creating a brand-new industrial ecosystem. Under this ecosystem, intelligent automated machines, advanced predictive analysis, and human-machine collaboration are deeply integrated to enhance productivity, efficiency, and reliability. The IIoT makes it possible to connect embedded modules and products into largescale systems, laying the basis for intelligent industrial monitoring.

Traditionally, industrial processes are monitored by online systems with alarming function. There are two kinds of industrial process monitoring systems: the manufacturing execution system (MES) and process control system. The process control system, which is more popular than the MES, monitors the states of industrial processes with configuration software, focusing on the online detection of machine failures and the change trend of key parameters.

The current process control system provides many modeling methods, namely, principal component analysis (PCA), kernel-PCA (KPCA), and support vector machine (SVM). During operation, the process control system collects the operational data continuously and selects the most suitable modeling method to predict faults online and judge whether it is necessary to issue alarms. However, the prediction accuracy of the current process control system is yet to be improved.

The IIoT-based control of industrial processes has better accuracy than the current process control system. But, the fault prediction is still hindered by the heavy presence of unknown parameters in the control system, which adds to the difficulty in mechanical maintenance. To solve the problem, this paper combines the artificial fish swarm algorithm (AFSA) and the particle filtering (PF) algorithm into the AFSA-PF algorithm based on the self-organizing state space (SOSS) model and verifies the effectiveness of the algorithm through simulation. The artificial fish school algorithm is a random search optimization algorithm that simulates the ecological behavior of fish schools in the natural environment. It includes four adaptive behaviors of fish schools: foraging behavior, grouping behavior, rear-end behavior, and random behavior. It has been used in many engineering fields and achieved good results.

With the dawn of the Fourth Industrial Revolution (Industry 4.0), the IIoT has emerged as a communication network that allows devices to be accessed easily without sacrificing security and reliability. In general, the IIoT consists of four layers, including a sensing layer, site management layer, network layer, and application layer (the copyright of Figure

The structure of the IIoT.

The sensing layer collects information from various devices, e.g., radio-frequency identification (RFID) readers, cameras, and sensors. In this layer, intelligent wireless systems with sensors can automatically perceive and exchange information between devices and control them in a remote manner.

The site management layer provides an external interface for the industrial data and manages the data locally. This layer is equivalent to a local dispatching and management centre.

The network layer mainly transmits messages and processes information. This layer connects everything together, allowing them to share information with each other.

The application layer adopts suitable technologies to optimize the production processes or industrial applications.

The IIoT is generally deployed in four phases: First, smart sensors collect the real-time industrial data anytime, anywhere. Second, the communication network uploads the collected data in real time. Third, the uploaded data are modelled and analysed based on big data, cloud computing, and data mining. Fourth, the industrial production is upgraded through information management and platform integration, making production more efficient, resource utilization more complete, and production cost lower.

The traditional monitoring systems of industrial processes mainly support online monitoring and early warning. The IIoT-based intelligent monitoring system emphasizes on the diagnosis and prediction of abnormalities through modeling the current states of industrial processes. To issue real-time alarms, the IIoT-based system pushes the alarm information to the relevant management and operation terminals via the mobile network. The distributed message queue middleware is adopted to deliver the alarm messages reliably in real time. All alarm messages are sent from the system to the middleware, according to the type and level of the information.

The materials and methods section should contain sufficient detail so that all procedures can be repeated. It may be divided into headed subsections if several methods are described.

Based on the Monte Carlo (MC) method and recursive Bayesian estimation, the PF provides a filtering method for nonlinear, non-Gaussian systems [

The basic idea of the PF algorithm is as follows: First, a set of random samples called particles are generated based on the empirical distribution of system state vectors. Then, the weight and position of the particles are updated continuously according to the measured data. Finally, the initial empirical distribution is corrected as per the updated information.

In essence, the PF algorithm approximates the probability distribution of correlations by discrete random measures, which are composed of particles and their weights, and updates the discrete random degree recursively. If the sample size is large, the MC method will be called to approach the true posteriori probability density function of the state variable.

At present, the PF algorithm has been widely applied in positioning and tracking [

For an industrial process monitoring system, the discrete equation of state can be expressed as_{k} is the state noise vector; _{k} is the mean system manoeuvre at time

The discrete observation equation of the system can be defined as_{k} is the observed vector;

The general nonlinear equation can be described as^{n} × ^{n} ⟶ ^{n} is the state evolution map; ^{n} × ^{m} ⟶ ^{m} is the measure mapping; and

The goal of process monitoring is to estimate the state based on the measured data _{k} at time

Normalizing the weight to

The weights are selected by importance sampling. If the set

If the importance density can be resolved as

Then, a new set

The posteriori probability density function can be expressed as

Substituting (

If _{k−1} and _{k}. In this case, only

The standard PF algorithm chooses the easiest achievable priori probability density as the importance density function:

Replacing (

Then, the weight

The posteriori probability density

It can be seen that, when

The pseudocode of the standard PF algorithm is given below (Algorithm

{

A particle

Prediction: Use equation of State (

Calculate particle weights:

Normalized weight,

Then, the minimum mean square estimate of the state vector at time

Resampling: A new set of particles

}

The PF algorithm was improved based on the SOSS model to control the industrial processes based on the IIoT. To begin with, the vector of the unknown parameters in the IIoT-based process control system is denoted as

We suppose the initial set _{j} is the centre of

Given the priori condition probability _{k} at time

Normalizing the weight to

{

A particle set

Prediction: Use equation of state to predict the unknown state

Calculate particle weights:

Normalized weight,

Then, the minimum mean square estimate of the state vector at time

Resampling:

}

In normal cases, the SOSS-based PF algorithm can effectively filter unknown parameters of the IIoT-based process control system. However, the performance of the algorithm depends heavily on the sampling quality, which is a subproblem of initial sampling. Unfortunately, the initial distribution of unknown parameters is not easy to determine. If the initial samples only have a few values in the concentration zone of posteriori distribution, it would be difficult for the SOSS-based PF algorithm to filter the unknown parameters well.

To solve the problem, the AFSA [

First, the search space

The relationship between the original space and subspaces.

Through the abovementioned process, the SOSS-based AFSA-PF algorithm was obtained. This global search algorithm can effectively estimate system states and derive a realistic distribution of unknown parameters. The pseudocode of the SOSS-based AFSA-PF algorithm is given below (Algorithm

{

For each subset

PREDICTION: Using Equation of state (

Calculate particle weights:

Normalized weight,

The results and discussion may be presented separately, or in one combined section, and may optionally be divided into headed subsections.

To verify its adaptability, the SOSS-based AFSA-PF algorithm was applied to estimate the state and identify the parameters of an IIoT-based process control system with unknown parameters. During the simulation, the error level of each sensor was adjusted: the observed noise was changed to

The unknown parameters identified by the SOSS-based AFSA-PF algorithm.

The system states can be described by the following nonlinear mathematical model:_{1} (_{2} (_{3} (_{4} (

In each subset, the particle

Based on the abovementioned artificial intelligence (AI) model, the proposed algorithm can be implemented in the following steps.

When the unknown parameter belongs to space

The objective function can be expressed as

Let ^{q} (^{l} in its perception range. If

Let ^{q} be the current state of an AF and _{f} be the number of AFs in other clusters in the perception range of the AF. Then, the centre of the neighbourhood of the AF can be described as

Otherwise, the AF will move as it does in the foraging process.

In our algorithm, a bulletin board is set up to record the optimal value of the current objective function. After each move, the AF compares its objective function

Resampling:

The local linearization of the abovementioned nonlinear system is equivalent to the model of the original nonlinear system:

The parameters of the correlation matrix are as follows:

Assuming that the initial state is

The upper bound of the corresponding system performance index can be obtained as

The designed controller was applied to the model of the original nonlinear system, and the simulation time was set to 5 s. The simulation results are displayed in Figures

The actual state response of the system.

The controlled state response of the system.

To verify its antijamming performance, the designed controller was simulated after the state vectors _{1} (_{3} (

The actual state response of the system under jamming signals.

The controlled state response of the system under jamming signals.

To verify its robustness to variable system parameters, the designed controller was further simulated after changing system parameters from

The actual state response of the system at

The controlled state response of the system at

From the abovementioned simulation results, the designed controller was found to keep the nonlinear system with unknown parameters stable and bring the system back to equilibrium state, despite the addition of jamming signals and the variation in system parameters. Changing the error level of sensors could affect the system error and also influence the identification of unknown parameters. The stronger the sensor noise, the greater the system error. However, the influence on unknown parameters is way smaller than the location error. As a result, the proposed algorithm could accurately estimate the estimation parameters.

The existing filtering algorithms for the IIoT-based process control system only work if the system model is deterministic. In real-world scenarios, it is very difficult to find an IIoT-based process control system that is truly deterministic. The model parameters of the system are often unknown, though their ranges might be identifiable. To eliminate the effect of the unknown parameters on the IIoT-based control of industrial processes, this paper develops a novel AFSA-PF algorithm based on the SOSS model. The SOSS-based AFSA-PF algorithm can effectively estimate system states, approximate the actual distribution of unknown parameters, and disclose the true value of the unknown parameters. With the aid of the proposed algorithm, the system model could reflect the actual states of the IIoT-based process control system. The research findings provide a good reference for applying AI techniques in industrial process control.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

This work was supported by High-Level Talents Foundation of Ankang University (Grant No. 2019AYQDZR01) and Ankang Science and Technology Research and Development Project (Grant No. AK2019SF-09).