The Online Identification of the Behaviour of Pollutants inside the Tunnel Tube

Abstract

A tunnel tube is a relatively small space that allows for the accumulation of gaseous and liquid substances containing harmful substances. Given this fact, a ventilation system is the most critical component of a tunnel’s technological equipment, greatly influencing its reliability and safe operation. The dynamic behaviour of pollutants in the tunnel tube is characterized by a significant stochastic component and changing parameters over time due to pressure, airflow, and atmospheric condition changes. This work addresses the issue of modelling individual parts of the tunnel tube for optimal tunnel ventilation control. It is necessary to create a model of a controlled system that is used for predicting process variables to calculate optimal control action. By using recursive identification methods in conjunction with a predictive controller, the proposed concept can be applied to numerous similar applications.

1. Introduction

Tunnels are constructed where it is necessary to overcome natural or artificial obstacles. They reduce the route length, improve its vertical and directional conditions, and preserve the environment above the tunnel in its original state. An essential role of tunnels is to increase transportation capacity and speed and reduce air pollution levels by appropriately locating the exits of ventilation units away from inhabited centres. When designing a tunnel, it is essential to make good use of technical means considering its long-term, trouble-free operation [1]. Technical conditions (TCs) and regulations provide solutions based on long-term experience for the design, engineering, implementation of technological equipment, and construction of road tunnels, ensuring that the tunnel is an economically and ecologically viable structure, guaranteeing a high level of safety for the general public [2]. European tunnels are equipped with all modern safety features required by EU Directive 2004/54 [3]. The tunnel has its own life, inevitably requiring smooth functioning and proper care. Increased attention to tunnel safety necessarily leads to the need for higher care and maintenance [4,5].

The tunnel tube is a relatively small space that allows for the accumulation of gaseous and liquid substance-containing pollutants. These substances can be harmful to the human body as well as to the construction materials and technological equipment of the tunnel. Pollutants are typically not the primary cause of tunnel incidents. In the event of a ventilation malfunction, the tunnel must be closed. The primary safety of the tunnel focuses on minimizing accidents within the tunnel. However, secondary safety must also be given attention. Tunnel closure redirects traffic, increasing the risk of accidents, which can be mitigated via secondary safety measures. The reliability and quality of ventilation influence secondary safety. It is the reason for solving the optimization problem of the ventilation. Article [6] deals with rail transport applications’ primary and secondary safety uses. In exceptional situations, such as accidents in tunnels, fire safety in road tunnels addresses ventilation and traffic management during emergencies and crisis scenarios. It is important to note that this article does not cover fire safety and primary safety. The fire safety is explored in publications [7,8,9].

The exhaust gases from automobiles are a source of carbon monoxide (CO), a highly toxic combustible gas. It is formed during the incomplete combustion of carbon and other carbon-containing compounds. Another product that is formed in combustion engines of automobiles is nitrogen oxide. Nitrogen oxide molecules are reactive and unstable; they react with oxygen in the atmosphere, forming toxic nitrogen dioxide (NO₂). NO₂ and nitric oxide (NO) are marked as a group of nitrogen oxides (NO_x). The units for the concentration of CO and NO_x are ppm (parts per million). More information is available in [10,11]. In light of these facts, the ventilation system is the most crucial component of the tunnel’s technological equipment, greatly influencing its reliable and safe operation. The selected ventilation system, its design, the choice of specific types of fans, and their control affect the energy consumption of the ventilation system and, thus, the operational costs of the tunnel.

In the case of ventilation based on physical parameters, fans are controlled according to the instantaneous values of carbon monoxide concentrations or visibility measured at individual points, for example, 200 m from the tunnel portal. The frequency of the ventilation system switches based on the immediate value of pollutant concentration, even if it is caused by a single vehicle with high emissions. The frequent and unpredictable activation of the ventilation system has an impact not only on increased energy consumption but also on the lifespan of the fans, which have a limited number of switching cycles. This novel study aims to create a suitable model of the behaviour of pollutants in the tunnel tube for use in the ventilation control system, aiming to save electrical energy and minimize the number of fan activations while complying with the defined limits for pollutant concentrations in the tunnel.

To achieve this objective, developing a model describing the behaviour of pollutants in the tunnel tube is essential. The input variables include personal and freight vehicles’ traffic intensity, speed, and meteorological influences (temperature, pressure, wind speed, etc.). The outputs are the concentrations of CO, NO, and OP. Opacity (OP) is a physical parameter that quantifies the degree of light non-transmittance through a material or medium, and it is typically denoted in units of 1/km.

2. Parametric Identification of the Behaviour of Pollutants in Individual Parts of the Tunnel Tube

Methods for parameter estimation allow determining the parameters of a model for a chosen structure from a sequence of measured input and output values. Identification methods assume the discrete measurement of signals, resulting in corresponding numerical sequences of input u(k) and output y(k) values.

This article focuses on the analysis and identification of the movement of harmful substances in the eastern tunnel section of the Mrázovka road tunnel located in Prague. Data analysis was carried out using modelling in the Matlab software environment (version 2022b, Mathworks, Natick, MA, USA). Offline stochastic models were created, and simulations and predictions of harmful substance concentrations in the tunnel were performed to select an appropriate parametric model structure. Data sources include personal and freight vehicles’ traffic intensity, speeds, concentrations of CO and NO_x, opacity (OP), airflow, and air speed. These are variables measured directly inside the tunnel via sensors. The system is described through relationships between input and output processes. The chosen procedure for estimating the dynamic system model involves several steps: determining the model’s structure, parameter estimation, and model verification. The program utilizes a database from measured traffic intensity, vehicle speeds, tunnel air speeds, harmful substance concentrations, and opacity inside the tunnel. The processed data were recorded over several days in the Mrázovka tunnel, with measurements taken twice a minute. The two-day database contains 5760 samples for each variable, respectively. Sensing principles are discussed in [12,13,14,15,16,17].

Various methods can be used to compute model parameters. Iterative and recursive least squares algorithms form the basis of parameter estimation [18]. Linear regression models describe the dynamical systems. There are many derived identification algorithms for pseudo-linear regression models, such as the Recursive Extended Least Squares algorithm (RELS) for models with Controlled Autoregressive Moving Average (ARMA) [19,20], the Least Squares Filtering Algorithm for Controlled ARMA (CARARMA) systems [21], Recursive Generalized Least Squares Parameter Estimation [22], Adaptive Forgetting Factor Recursive Least Square Algorithm [23], and others.

The term parametric identification refers to creating a model describing the dynamic behaviour of pollutants in a tunnel. The term tunnel section means a tunnel section with defined input and output variables. The system identification procedure is depicted in Figure 1.

The selection of an appropriate model structure is the most crucial part. This selection must be based on understanding the identification method and the information about the identified system. Once the model structure has been determined, the chosen identification method will provide us with the precise form of this structure and the exact procedure for determining its parameters.

A fundamental question is whether it is good enough for the intended use. Testing the suitability of the model is referred to as model validation.

System identification is an integral part of every control design and deals with the problem of creating reliable mathematical models of dynamic processes based on observed input–output data (Figure 2). The input variable is denoted as u(t), the output variable as y(t), the output predictions as ŷ(t), and the estimated parameters as $\widehat{\theta }\left(t\right)$. The results of the identification determine the achieved quality of control.

General aspects of model selection include the following:

• Flexibility: Using a model structure that provides good properties for describing the systems. It can be achieved using more parameters or their “strategic” placement.
• Economy: The model structure should be as economical as possible, i.e., the use of a minimum number of parameters, because their number determines the complexity of the calculations (computational performance of the hardware) and, at the same time, in many cases, only unnecessarily complicates the model.

3. Methods of Recursive Identification

Recursive identification methods, or online methods, construct a system model based on past observations to the present moment. In terms of describing changes in concentrations of harmful substances within a tunnel tube, it is appropriate to create a model of this system for predicting and designing optimal ventilation control using the developed model. Since online identification is employed, it must also be appropriately automated. The algorithm must select an appropriate model form (time delay, order of differential equations, etc.), determine the initial parameters, compute the residuals, and assess the degree of agreement between the system and the model. Utilizing a larger volume of data will create more accurate models.

The recursive algorithm must have initial conditions set for θ(0) = 0 and P(0) = cI, where c is an arbitrary constant (e.g., 10⁵), and I is an identity matrix.

Identification algorithms designed for ‘real-time systems’ serve multiple purposes, including monitoring time-varying parameters, enabling adaptive control, supporting filtering, prediction, signal processing, detection, and diagnostics. However, many data-driven identification methods still need to be improved for real-time applications, necessitating appropriate algorithmic reformulation to achieve an efficient procedure. According to the literature [24,25], the recursive identification method can be expressed in the following form:

$$\begin{gathered} \epsilon \left(k+1\right)=y\left(k+1\right)-w^T\left(k+1\right)\cdot \widehat{\theta }\left(k\right) \\ \widehat{\theta }\left(k+1\right)=\widehat{\theta }\left(k\right)+P\left(k\right)\cdot w\left(k\right)\cdot \epsilon \left(k\right) \\ P(k+1)=P(k)-\frac{P\left(k\right)\cdot w(k+1)\cdot w^T(k+1)\cdot P\left(k\right)}{1+w^T(k+1)\cdot P\left(k\right)\cdot w(k+1)}\cdot \end{gathered}$$

(1)

Identifying a system is the capability of an identification method to find unbiased parameter estimates. We assume that the structure of the identified system aligns with the model structure. The capacity to identify the system for model creation depends on the invertibility of the covariance matrix and the type of input signal u(k). For the covariance matrix, the following relationship holds:

$$P^{-1}(k)={\sum }_{i=1}^{k}w\left(i\right)w^T(i).$$

(2)

From the provided Equation (2), it is evident that if k ≥ n, where n is the dimension of the data matrix (data vector), the covariance matrix will be invertible. This inequality is a necessary but not sufficient condition because the vector w(k) may not be what is known as ‘identification-rich’. An ARX model described by the equation in the form of (4) is considered for elucidation.

$$y(k)=-{\sum }_{i=1}^n{a}_{i}y(k-i)+{\sum }_{i=1}^n{b}_{i}u(k-i)+\varsigma (k).$$

(3)

The conditions for the convergence of parameters in the recursive least squares method are as follows [24]:

• Polynomials A and B are coprime;
• The system is stable;
• The input u(k) is information-rich, of at least order 2n.

For unstable systems, stabilization via a controller is required first. In the case of a closed-loop control system, information richness is not met because u(k) is generated as a linear combination of the data vector w(k). Therefore, parameter convergence may not be guaranteed. Convergence can be ensured by adding an external signal v(k) to the input signal u(k). The external signal must be information rich, with a minimum order of 4n.

The primary recursive identification method (Equation (1)) cannot be applied to systems with changing parameters, such as models describing the behaviour of harmful substance concentrations in a tunnel tube. For this purpose, we modify the algorithm by introducing a parameter denoted as the symbol λ for exponential and directional forgetting.

3.1. Modification of the Recursive Least Squares Method

To ensure stability, we derive a method with exponential forgetting. This modified parameter estimation method allows for tracking parameters that change over time [26]. The modified objective function is as follows (4):

$$J(\widehat{\theta })={\sum }_{i=1}^k{\lambda }^{k-i}{\left(y\right(i)-w^T(i\left)\widehat{\theta }\right(k\left)\right)}^2,\hspace{0.17em}\hspace{0.17em}0<\lambda \le 1.$$

(4)

The result is a recursive algorithm with exponential forgetting (5).

$$\begin{gathered} \epsilon \left(k\right)=y\left(k\right)-w^T\left(k\right)\widehat{\theta }\left(k-1\right) \\ \widehat{\theta }\left(k\right)=\widehat{\theta }\left(k-1\right)+P\left(k\right)w\left(k\right)\epsilon \left(k\right) \\ P(k)=\frac{1}{\lambda }\left(P(k-1)-\frac{P\left(k-1\right)w\left(k\right)w^T\left(k\right)P\left(k-1\right)}{\lambda +w^T\left(k\right)P\left(k-1\right)w\left(k\right)}\right). \end{gathered}$$

(5)

This modified algorithm emphasizes agreement with current data and reduces the influence of previous data, meaning it gradually forgets older data. However, a secondary undesirable effect arises—sensitivity to noise, particularly when the parameter λ is increased. The choice of λ is determined via a compromise between the ability to track changing parameters and the allowed sensitivity to noise. In most cases, the parameter λ is chosen in the interval <0.97, 0.995>, although the correct choice depends on the nature of the identified system and the sampling period. The number of stored samples can be approximately determined using the relationship, $\frac{1}{1-\lambda }$, corresponding to the time constant associated with the parameter λ. This algorithm can be used if the system parameters change slowly. The disadvantage of the derived algorithm (Equation (5)) with exponential forgetting is that if the input signal has small or zero values (not identifiable), the covariance matrix increases exponentially with time when λ < 1. This phenomenon is called wind-up estimation. The solution is not to update the covariance matrix when the input variable values u(k) are close to 0. At first, an s-function was written and used in Simulink to verify the operation of the derived algorithm. However, using the s-function was unsuitable because the compiler could not create code in C or C++ code when used in the Simulink model. Therefore, the s-function was rewritten as a Matlab function. The block titled ‘estimator_d’ is a subsystem within Simulink and contains a function created by the authors, in which all algorithms derived in this article are programmed. First, the algorithm was tested on deterministic system models with known parameters. The Simulink simulation scheme is in Figure 3.

The representation of the simulation results of the recursive least squares method with exponential forgetting is shown in Figure 4. The two lower graphs present the behaviours during parameter variations in more detail. Parameters a₀ to a₂ have negative signs because the graph shows the vector of parameters.

The algorithm tracks changes in the system parameters but exhibits significant oscillations even with small parameter changes. Due to its noise sensitivity, it is unsuitable for identifying stochastic systems. The influence of a disturbance variable acting on the identified system’s output causes the estimated parameter values to oscillate (Figure 5).

One possible modification is to turn off identification selectively if the estimated parameters are correct. The size of the prediction error is monitored. The parameters will not be changed if the prediction error is within an acceptable range. A new parameter α(t) is defined:

$$\alpha (t)=\left\{\begin{array}{l}1\hspace{0.17em}\hspace{0.17em}if\hspace{0.17em}\frac{1}{1+w^T\left(k\right)\cdot P\left(k\right)\cdot w\left(k\right)}\cdot {\epsilon }^2(t)>{\epsilon }^2(t)>0\hspace{0.17em}\\ 0\hspace{0.17em}\hspace{0.17em}in the opposite case\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\end{array}\right.$$

(6)

The parameter ε is a small number. The parameter α(t) was added to Equation (5):

$$\begin{gathered} \widehat{\theta }(k+1)=\widehat{\theta }\left(k\right)+\alpha \left(t\right)P\left(k\right)w\left(k\right)\epsilon \left(k\right) \\ \epsilon (k+1)=y\left(k\right)-w^T\left(k\right)\widehat{\theta }\left(k\right) \\ P\left(k+1\right)=\alpha \left(t\right)\frac{1}{\lambda }\left(P\left(k\right)-\frac{P\left(k\right)w\left(k\right)w^T\left(k\right)P\left(k\right)}{\lambda I+w^T\left(k\right)P\left(k\right)w\left(k\right)}\right)+NOT\left(\alpha \left(t\right)\right)P\left(k\right). \end{gathered}$$

(7)

This modification ensures that the covariance matrix and the estimated model parameters will not be changed if the system’s outputs match the model’s outputs. This principle also saves computational resources for the control system. If no new information is received for an extended period, the covariance matrix may no longer be positive definite, causing the algorithm to crash. Therefore, monitoring the trace of the covariance matrix is generally recommended. Stability is ensured via a recursive least squares method with directional forgetting.

3.2. Recursive Least Squares Method with Directional Forgetting

A recursive least squares method with directional forgetting (DF), which forgets only in the direction of new information, was derived to ensure stability. This method has better convergence properties. The estimate forgets old information and ensures convergence of the estimates while preventing significant parameter changes. It is suitable for identifying systems with parameters that do not change abruptly.

$$\begin{gathered} \widehat{\theta }(k+1)=\widehat{\theta }\left(k\right)+P\left(k\right)w\left(k\right)\epsilon \left(k\right) \\ \epsilon (k+1)=y\left(k\right)-w^T\left(k\right)\widehat{\theta }\left(k\right) \\ P\left(k+1\right)=P\left(k\right)-\frac{P\left(k\right)w\left(k\right)w^T\left(k\right)P\left(k\right)}{{\tau }^{-1}\left(k\right)+w^T\left(k\right)P\left(k\right)w\left(k\right)}. \end{gathered}$$

(8)

The equation gives the directional forgetting factor:

$$\tau (k)={\lambda }^{\prime }-\frac{1-{\lambda }^{\prime }}{w^T\left(k\right)P\left(k\right)w\left(k\right)},$$

(9)

where λ′ can be chosen as in the algorithm with exponential forgetting [19].

Figure 6 shows the parameter estimate trajectories obtained with the recursive least squares method with directional forgetting.

The analysed behaviour exhibits more minor oscillations for small parameter changes, which is the main criterion for accurately tracking parameter changes in a system over time for proper model updating. For comparison, the plots also depict the behaviour for significant parameter changes in the system. Compared to the previous algorithm, the estimates are smoother with less oscillation, but it takes longer for the parameters to be accurately estimated.

The influence of the disturbance quantity on the output is shown in Figure 7.

The influence of disturbances acting on the output quantity of the identified system will cause a slight fluctuation in the values of the estimated parameters.

3.3. Exponential Forgetting and Resetting Algorithm

The recursive least squares method with exponential forgetting and resetting (EFRA—Exponential Forgetting and Resetting Algorithm) is a modification of the recursive method of least squares—imposes upper and lower bounds on the direction of the covariance matrix while concurrently preserving the influence of the weighting factor λ [27]. The algorithm is described in Equations (10) and (11):

$$\begin{gathered} \widehat{\theta }(k+1)=\widehat{\theta }(k)+\alpha L(k)\epsilon (k) \\ \epsilon (k+1)=y(k)-w^T(k)\widehat{\theta }(k) \\ L(k+1)=\frac{P(k)\widehat{\theta }(k)}{\lambda +{\widehat{\theta }}^T(k)P(k)\widehat{\theta }(k)} \\ P\left(k+1\right)=\frac{1}{\lambda }\left(P\left(k\right)-L\left(k\right)\widehat{\theta }\left(k\right)P\left(k\right)\right)+\gamma I-\gamma P{\left(k\right)}^2. \end{gathered}$$

(10)

The adjustable parameters in Equation (10) are determined according to expressions (11).

$$\begin{gathered} {\sigma }_{\mathrm{m}\mathrm{i}\mathrm{n}}I\le P\left(k\right)\le {\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}I\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\forall k \\ {\sigma }_{\mathrm{m}\mathrm{i}\mathrm{n}}\approx \frac{\gamma }{\alpha -\frac{1-\lambda }{\lambda }},\hspace{0.17em}{\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}\approx \frac{\frac{1-\lambda }{\lambda }}{\gamma }+\frac{\gamma }{\frac{1-\lambda }{\lambda }} \\ \alpha =0.5,\hspace{0.17em}\gamma =0.005,\hspace{0.17em}\lambda =0.95 \end{gathered}$$

(11)

According to the trajectories of the estimated parameters in Figure 8, a change can be seen compared to the previous estimates, which are shown in Figure 4 and Figure 6. Compared to previously tested methods, the time for the stabilization of the parameters is significantly reduced, and fluctuations during parameter changes are minimized.

The disturbance affecting the output variable of the identified system causes only slightly more significant fluctuations in the estimated parameter values (Figure 9) compared to the previous method.

Although the recursive least squares method with a directional forgetting algorithm exhibits greater resilience to disturbances, the application of the Recursive Least Squares Method with Exponential Forgetting and Resetting is well suited for characterizing the behaviour of pollutions in a tunnel environment because it guarantees rapid parameter convergence and minimal oscillations during parameter changes. The coefficients of the numerator polynomial are denoted as b₀ through b₃, and the denominator polynomial coefficients are a₀ through a₂, with a₃ equal to one. The transfer function takes the form:

$$F\left(z\right)=\frac{b_3{z}^3+b_2{z}^2+b_{1}z+b_0}{a_3{z}^3+a_2{z}^2+a_{1}z+a_0}.$$

(12)

The simulation in Figure 10 illustrates the algorithm’s capability to track the changing parameter a₀ as a continuous function of time.

Parameter a₀ decreases from 0 to −0.1 for 1 s and then increases from −0.1 to 0.1 until 3 s. The legend denotes the latest estimations, which align accurately with the actual values.

It is necessary to analyse the created models and verify their correctness. Several methods were used to determine the quality of the model: the percentage of agreement (for graphical comparison of outputs), residual test, mean squared error (MSE), and final prediction error (FPE). All these methods are available in Matlab [28].

The following chapters focus on estimating parameters using real data measured in the tunnel.

4. Results

In the previous chapters, the functionality of algorithms was verified on deterministic systems and systems affected by disturbances as well. The disturbances act at the system’s output before the sensors and are caused by air turbulence generated via passing vehicles and changes in pressure inside the tunnel tube.

Figure 11 illustrates the measured data inside the tunnel tube during one day.

The Simulink scheme for estimations of parameters is shown in Figure 12. The identification procedure for other input–output data was realized in the same way.

Figure 13 illustrates the results of the estimations of parameters utilizing real measured data inside the tunnel over two days. The EFRA was employed for this analysis. The legend also presents the values of the latest estimations.

The given courses were obtained under the following settings: the used algorithm was the least squares method with exponential forgetting and resetting, with a weighting factor λ was set to 0.97, α was 0.6, γ was 0.005, σ_min was 0.001, and σ_max was 10. When λ was changed to 0.94, the courses of estimated parameters exhibited increased oscillations, as shown in Figure 14.

In Figure 15, the upper graph compares the simulated CO concentrations inside the tunnel tube with measured data. The bottom graph shows the difference between measured and simulated outputs.

Determining the structure of the model is an essential step for correctly identifying the behaviour of pollutants in the tunnel tube. Figure 16 shows the estimation of parameters that are reduced by one parameter.

An appropriate change in the number of parameters will reduce the deviation of the simulated CO concentrations compared to the measured values, i.e., better describes the identified system (Figure 17). After changing the structure of the model, the onset of parameter estimation was accelerated. This improvement is also due to the inclusion of a real input–output delay in identification.

The mentioned algorithms can be modified and used to identify multidimensional systems. For example, the article [29] solves the parameter identification problems for multivariable output-error-like systems with coloured noises.

5. Implementation

The “B&R Automation Studio Target for Simulink” toolbox was used to implement the continuous identification method into the PLC (Programmable Logic Controller). Inputs and outputs were added to the scheme in Simulink according to Figure 18. Then, the model configuration block (B&R Configuration) was added.

In the model, we left the possibility to identify the deterministic system described by the transfer function with the possibility to switch to external inputs and outputs of the identified system.

In the Model Configuration tab, the C language was selected, and in the basic settings, a project was selected in which the continuous identification algorithm was implemented (Figure 19).

The Simulink model from Matlab was successfully converted into C source code in Automation Studio, as depicted in Figure 20a. The generated program is automatically inserted into the PLC project in Automation Studio, and the entire project is compiled before being transferred to the target system (PLC) using the transfer command. The generated program is assigned to the processor in the current hardware configuration. The functionality of the automatic code generation can be easily verified by opening the Watch window in Automation Studio after loading it into the PLC. The result can be seen in Figure 20b) in the variable monitoring window (Watch). The variable Input1 is an input that can be modified using an external source or monitoring window. The parameters were correctly estimated for the internal deterministic system.

For the implementation of derived identification algorithms and control algorithms, the programmable logic controller (PLC) was chosen, particularly the type PanelPC by the Austrian company B&R, model 5PPC3100-KBU2 [30]. Its primary specifications are as follows: Processor type and Clock frequency: Intel i5-7300U, a dual-core processor operating at a clock frequency of 2.6 GHz; Memory: 16 GB of DDR4 Synchronous Dynamic Random Access Memory (SDRAM); Storage: CompactFlash-based “CFast” industrial Hard Disk Drive with a storage capacity of 128 GB; Communication Interfaces: Ethernet, POWERLINK, USB ports, and RS232; Automation Panel (Display) 12.1” WXGA TFT—1280 × 800 pixels (16:10)—Multi-touch (projected capacitive).

The computational power of this PLC is deemed sufficient to handle the computational demands of both solving the system identification algorithms and predictive algorithms. The cycle time of program execution is 2 ms (can be configured from 0.4 ms to several seconds).

6. Discussion

Currently, in most cases of tunnel ventilation systems, conventional control algorithms are employed (such as PID controllers). This choice is due to their ease of implementation within control systems and compliance with ventilation requirements. However, when we aim to address the matter of optimal control concerning specific criteria, such as the minimization of electrical energy consumption (eliminating fan activations based on a one-time exceedance of harmful substance concentration limits), ensuring ventilation pre-emptively before approaching limit exceedances, accounting for significant time constants and dynamic system time delays, handling mutual interactions among various inputs and outputs, considering constraints on input and output variables and system parameters, and factoring in system disturbance, we must employ alternative forms of controllers capable of accommodating these aspects within their algorithms. Over the past few decades, significant progress has been made in this regard, and these approaches are currently implemented across various industrial and transportation applications. The term “model predictive control” does not denote a specific control strategy but rather a broad spectrum of control methods that explicitly utilize a process model for computing control signals by minimizing a cost function. This article primarily focuses on constructing a system model. Therefore, this work addresses the modelling of specific segments of the tunnel tube that characterize air pollution levels. The criteria for an appropriate recursive identification algorithm include stability, parameter convergence, resistance to disturbances, adaptability, efficiency, and real-time capability.

Controlling the ventilation in the tunnel tube according to predicted traffic data assumes a close and logical connection between traffic intensity and pollutant concentrations. Predictions with the model eliminate a one-time increase in pollutant concentrations and eliminate short-term erroneous measurements of pollutant concentrations. The influence of the jet fan on the pollutants inside the tunnel is described in [31]. Jet fans are installed on the ceiling or side walls of the tunnel to create an air stream. The design of optimal ventilation control in the tunnel using a controller that will use a model of the controlled system (for example, a predictive MPC controller uses a model of jet fan influence on pollution, as well as pollution model as measured disturbances) when calculating control action must ensure that the required limits of pollutant concentrations are not exceeded. The limit values for concentrations of harmful substances for regular operation recommend that the air quality values in the tunnel tube not exceed 70 ppm for CO and 5 km⁻¹ for OP. If these limits are observed, it is not necessary to control NO_x concentrations because it is assumed that the values of nitrous gases will not exceed the limits. In the standards, the limit for NO₂ ranges from 0.4 to 1 ppm, calculated as a 15 min moving average of variable across the entire tunnel [32]. From this point of view, it is sufficient to create two models, one for CO and the second for OP.

7. Conclusions

It is necessary to analyse and identify a specific tunnel to achieve optimal ventilation control within the tunnel. In order to apply the proposed algorithms to other tunnels, this study includes the derivation, description, and implementation of ongoing identification algorithms. The simulations and predictions of pollutant concentrations in the tunnel were conducted via modelling. The simulation results confirm the accuracy of the developed models that describe the behaviour of pollutants in the tunnel. The proposed approach enables the solution of various application problems encountered in practice.

The EFRA emerges as a suitable online identification method for describing the behaviour of pollutants within the tunnel tube. This suitability arises from its rapid parameter convergence, minimal oscillations during parameter adjustments, and resilience to disturbances. The analysed behaviour exhibits smaller oscillations in response to minor parameter variations, which is the principal criterion for accurately tracking parameter changes within a system over time for effective model updates. After verifying in Matlab-Simulink, the algorithm was successfully implemented into the PLC. The utilization of EFRA for predicting pollutant concentrations in tunnel has not been previously documented in any scientific articles. Furthermore, this article underscores the potential for employing new, robust industrial control systems that facilitate the implementation of modern methods for online identification and predictive algorithms.