Predictive control of slurry pressure balance in shield tunneling using diagonal recurrent neural network and evolved particle swarm optimization

Automation in Construction 107 (2019) 102928

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Automation in Construction journal homepage: www.elsevier.com/locate/autcon

Predictive control of slurry pressure balance in shield tunneling using diagonal recurrent neural network and evolved particle swarm optimization

T

Xiaofei Li, Guofang Gong

⁎

State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China

ARTICLE INFO

ABSTRACT

Keywords: Shield tunneling Slurry pressure balance Model predictive control Diagonal recurrent neural network Evolved particle swarm optimization Time delays Logical control sequence

Establishing the balance between slurry supporting pressure and expected water-earth pressure is an important criterion to ensure excavating face stability in shield tunneling. To overcome the inaccuracy and hysteresis of manual operations, this paper presents a model predictive control (MPC) system for the slurry pressure balance during construction through effectively regulating the slurry circulation and air pressure holding systems according to geological conditions. The MPC structure consists of a diagonal recurrent neural network (DRNN) that approximates the complex relationship between slurry pressure and tunneling parameters, an optimizer which produces the optimal air pressure and slurry level based on the multi-step ahead predictions, and an evolved particle swarm optimization (EPSO) algorithm. The proposed EPSO can update the structure and weights of DRNN concurrently to better cater to the changeable stratum. The optimizer can excellently compensate the time delays in slurry pressure regulation by incorporating the logical control sequence of actuator systems into the EPSO procedure. The simulation results demonstrated that the presented approach can accurately track the desired water-earth pressure and significantly enhance the robustness of slurry supporting system in tunneling, and the novel EPSO also performed higher convergence speed and precision than the classic algorithms used for comparison.

1. Introduction As the hinge of transportation network and underground engineering, tunnels have significant benefits in expanding urban space, relieving traffic congestion and exploiting natural resources. Because of higher excavation efficiency, better project quality and environmental friendliness, shield machine as a type of technology-intensive engineering equipment is widely used in tunnel construction. Moreover, equipped with the excellent supporting ability and stratum adaptability, slurry shield machine is playing an increasingly important role for the construction of riverbed tunnels and other specific underground facilities, especially for the high-permeability and low-viscosity strata [1]. The principle of the slurry shield tunneling is shown in Fig. 1, the bentonite suspension, pumped into the slurry chamber by feeding pumps through the slurry feed line, is used for supporting and stabilizing the excavating face and mixing with the excavated material. Meanwhile, the mixture in the connected chamber is exhausted by discharging pumps through the slurry discharge line and transported to the slurry disposal station. In order to keep the excavating face stability in tunneling, it is necessary to establish the effective balance between ⁎

the desired water-earth pressure and the actual slurry supporting pressure, where the former mainly depends on the geological and hydrological conditions and the latter is affected by the slurry level, air pressure and other shield operation parameters. To sustain the slurry pressure balance, present operators usually regulate the shield operation parameters based on the engineering experience which is often suffering from inaccuracy and hysteresis. Therefore, effectively identifying the complex relationship between the actual slurry supporting pressure and the shield operation parameters is crucial and indispensable for slurry pressure adaptive control. It is also the primary basis to achieve slurry shield tunneling automatically, efficiently and safely. To keep the tunneling face stability and avoid ground deformation in the process of shield construction, at present many researchers have taken considerable attention to the intelligent control based on artificial learning model and mechanism analysis. Zhou et al. [2] proposed an Elman neural network (a fully connected recurrent neural network with heavy computational burden) based predictive control system for air chamber pressure in slurry shield tunneling, where the desired air pressure was directly calculated according to the active and passive soil pressure. However, on the one hand, the actual slurry supporting pressure on the excavating face is not only depended on the air

Corresponding author. E-mail address: [email protected] (G. Gong).

https://doi.org/10.1016/j.autcon.2019.102928 Received 11 December 2018; Received in revised form 3 July 2019; Accepted 11 August 2019 0926-5805/ © 2019 Elsevier B.V. All rights reserved.

Automation in Construction 107 (2019) 102928

X. Li and G. Gong

Water-earth Pressure

speed adjustment. Nevertheless, the regulation of slurry supporting pressure in slurry chamber often suffers from time delays because of long-term slurry circulation. Therefore, based on the clay stratum and soil plasticized assumptions, the control models presented in above researches are unsuitable for slurry pressure balance control with changeable geological conditions and complex time-variant dynamics. Besides, the structure of these models were mainly determined by extensive offline experiments and cannot automatically evolved online according to the actual strata. This weakness also makes the predictive control system easily affected by the geological changes and confines the model application. The artificial neural networks (ANNs) were not only widely used in modeling and control of complex nonlinear systems [18–21], but also proverbially applied to forecasting the important parameters for shield tunneling [22–25]. According to the rock tests and construction data, both PSO based ANN and imperialism competitive algorithm based ANN were developed and used for predicting the penetration rate of tunnel boring machine (TBM) and both the models produced higher determination coefficients in [26]. The ANN was also used to forecast the number of consumed TBM disc cutters in [27] and the radial basis function neural network based time series analysis was employed to estimate the next-cycle production rates during construction in [28]. As we all known, these static feed-forward neural networks cannot deal with the time-variant processes effectively. However, owing to the inherent temporal operation abilities, the utilization of recurrent neural networks (RNNs) is more and more common in the control of complex time-varying systems [29–36], including the real-time prediction of TBM operation parameters [37]. Meanwhile, as one of the simplest and easily implementing RNNs, the diagonal recurrent neural network (DRNN) was also extensively used in nonlinear dynamic system control and industry areas [38–41], involving air-fuel ratio control of engine [42], positioning control of quadrotor [43], terrain parameters identification of wheeled mobile robot [44], wind speed and solar irradiation prediction [45,46], and so forth. All results reported in these papers demonstrated the superiority of DRNN in confronting time-varying targets. As the comparative research shown in [47], the DRNN model also exhibited stronger robustness and approximation ability for dynamic nonlinear system identification than multilayer feedforward neural network and nonlinear autoregressive neural network. Therefore, considering the requirements of response speed and accuracy for slurry pressure balance control, the DRNN was employed to identify the complex slurry supporting system in this study. In order to establish the effective balance between desired waterearth pressure and slurry supporting pressure on tunneling face, this paper proposed a reliable model predictive control system to produce the desired air pressure and slurry level timely, both of which are the major control variables for slurry pressure balance. Compared with the previous researches on supporting pressure balance control in shield tunneling, this paper has several core contributions which are described as follows. Firstly, improving the accuracy and relieving the computational burden of DRNN-based slurry pressure identifier through input feature analysis to select the highly correlated operation parameters. Secondly, presenting an evolved particle swarm optimization (EPSO) algorithm to update the topology structure and synaptic weights of DRNN model concurrently, so that the identifier can adapt to the geological changes automatically and robustly. Thirdly, the optimization model of control variables was established based on the multi-step ahead predictions of slurry pressure and as a result, the proposed MPC system can track the desired water-earth pressure effectively. At last, incorporating the logical control sequence between slurry circulation system and air pressure holding system into the EPSO implementing procedure for the optimization model, so as to inhibit the time delays and produce more applicable control laws for slurry pressure regulation system. The continuation of this paper is arranged as follows: Section 2 illustrates the model predictive control system for slurry pressure

Slurry Supporting Pressure Slurry Feed

Air Chamber Air Pressure

Slurry Level Bulkhead

Slurry Discharge Excavating Face

Slurry Chamber

Fig. 1. Principle of slurry shield tunneling.

pressure, but also influenced by the slurry level and other operation parameters. So it is unreasonable to derive the desired air pressure only from the expected water-earth pressure without considering the actual operating conditions and system coupling. Moreover, in the practical process of shield tunneling, the air pressure holding system usually keeps the actual air pressure balanced with the desired one automatically rather than regulating any other shield operation parameters. On the other hand, the capability of air pressure holding system to maintain slurry pressure balance is limited by the reserved space volume of air chamber for the compressed air. Namely, it is incompetent to guarantee slurry shield safely tunneling merely through air pressure control, especially for the large-diameter slurry shield machine. The discussed faultiness also exists in [3,4], which respectively employed digital incremental proportional-integral-derivative (PID) controller and fuzzy self-adaptable PID controller to adjust slurry supporting pressure based on the pre-defined slurry level and calculated air pressure, without considering the real-time shield operation parameters. Given the dynamic models of slurry circulation and propulsion systems, Li et al. [5] proposed a predictive function controller to regulate slurry pressure for the direct-type slurry shield machine (Japanese style without air chamber), which is not suitable for the indirect-type (German style with air chamber) used in this paper. It is also incapable for the mathematical models to effectively ascertain the complex relations between slurry supporting pressure and slurry circulation parameters. In addition, the least squares support vector machine (LS-SVM) was employed to forecast the earth pressure and establish the optimization model of control variables solved by particle swarm optimization (PSO) for the earth pressure balance (EPB) during shield tunneling in [6], and a nonlinear LS-SVM predictor combined with an improved ant colony optimizer was used for real-time EPB control in [7]. Considering the tunnel face stability in EPB shield construction, Shao et al. [8] used several back-propagation neural networks to predict multi-point earth pressure and calculate the normal vector angle, then derived the optimum screw conveyor speed from PSO by minimizing the difference between the predicted values and the desired one. For the EPB control, neural networks were also considered in [9–12], model predictive control was used in [13], mechanism analysis was combined with optimization algorithm in [14,15], nonlinear adaptive control method via Lyapunov back-stepping approach was presented in [16] and the fuzzy immune control method was applied in [17]. According to the principle of EPB shield tunneling, the soil pressure of working chamber can be regulated timely through the screw conveyor discharge and advance 2

Automation in Construction 107 (2019) 102928

X. Li and G. Gong

Hs

Slurry-level Sensor Slurry Shield

Hso Pd

Slurry Circulation System

MPC

Air Chamber

OP

Slurry Chamber

Ps

System Pao

Air Pressure Holding System

Pa

Air-pressure Sensor

Ps

Slurry-pressure Sensor

Fig. 2. The structure of slurry pressure balance control system.

balance; Section 3 establishes the slurry pressure identifier using DRNN model and accomplishes feature analysis; Section 4 proposes the EPSO algorithm and specifies the training procedure of DRNN identifier; Section 5 presents the predictive controller and elaborates the tuning rules for the control variables using the customized EPSO method; Section 6 includes simulation analysis and discussion; Section 7 concludes the researches in this paper.

For the purpose of keeping the slurry pressure balance on excavating face, an optimizer of control variables (CV) is established and solved using an evolved particle swarm optimization (EPSO) algorithm through minimizing the deviation between the desired water-earth pressure (Pd) and the predicted slurry supporting pressure (Ps ). As a randomization based swarm intelligence algorithm, the proposed EPSO method in this paper can calculate the optimal air pressure and slurry level effectively, taking into account the logical control sequence between the slurry circulation system and the air pressure holding system. Besides, this paper uses a diagonal recurrent neural network (DRNN) to provide the multi-step ahead predictions of the slurry supporting pressure based on the operation parameters (OP) and control variables, which can flexibly and accurately identify the nonlinear dynamic processes with time delays. The topological structure and synaptic weights of DRNN model are evolved simultaneously by the EPSO, so that the identifier can effectively adapt to the changeable geological and geotechnical conditions.

2. Control system of slurry pressure balance To overcome the hysteresis and inaccuracy of manual operations in shield tunneling, a model predictive control (MPC) system for slurry pressure balance is proposed in this section and its principle is shown in Fig. 2, where Pd is the desired water-earth pressure, OP is the slurry shield operation parameters, Hs is the actual slurry level, Pa is the actual air pressure, Ps is the practical slurry supporting pressure, Hso is the optimal slurry level, and Pao is the optimal air pressure. During the shield construction, the optimal slurry level and air pressure are derived online from the MPC system based on the desired water-earth pressure and the operation parameters obtained from the data collection systems. Then as the reference, the optimal variables are used to regulate the slurry circulation and air pressure holding systems, so that the slurry supporting pressure can be restricted into an acceptable range to maintain the tunneling face stability. The MPC system consists of a controller that provides optimal control laws for the actuator systems and an identifier that approximates the nonlinear timevariant dynamics between slurry supporting pressure and shield operation parameters, and its structure is depicted in Fig. 3.

-

It is recognized that the feedforward neural network as a static model is unable to deal with consecutive time-varying events without the aid of tapped delays which usually requires some inaccessible knowledge, such as the order of complex systems. However, the recurrent neural network as an important dynamic mapping tool is more suitable for the nonlinear temporal process modeling and can be used to effectively solve the time-delayed problems and store the information for later use. In this paper, considering the time consumption and computational burden of MPC system for the dynamic process in shield tunneling, a diagonal recurrent neural network (DRNN) as one of the simplest recurrent neural networks (RNNs) was applied to identifying the slurry supporting system. Though without interlinks among the hidden neurons, the DRNN model with considerably fewer parameters has the similar black-box mapping abilities compared with the fully connected RNNs. The presented DRNN identifier has less computational requirements and can also satisfy the demanded accuracy of slurry pressure balance control system concurrently.

+

3.1. Diagonal recurrent neural network

Identifier

Optimizer

DRNN

EPSO

Controller

TDL

TDL

+

3. DRNN based slurry pressure identification

EPSO

The DRNN architecture used for slurry shield modeling, suggested by Chao-Chee Ku [48], consists of one input layer, one hidden layer with self-feedback sigmoid neurons and one output layer with one linear neuron. As shown in Fig. 4, the input layer and the hidden layer of DRNN model contain n and m nodes excluding a bias, respectively. Equipped with sigmoidal activation function and unit-time delay selffeedback, the hidden neurons can benefit the model with significant capabilities in timing management and dynamic mapping.

Sensor

Slurry Shield Fig. 3. The structure diagram of MPC system. 3

Automation in Construction 107 (2019) 102928

X. Li and G. Gong

1

particle swarm optimization algorithm was presented to train the DRNN model, which can update the weights and hyper-parameters (the number of hidden neurons in this case) concurrently.

1 y(k)

S

3.2. Input feature analysis The selection of input features for the slurry pressure identifier, which has a significant effect on the prediction performance of DRNN model, was based on the shield tunneling mechanism and the in-site data statistical analysis. As the construction principle of slurry shield machine discussed above, it is obvious that the pool of most important candidate input features, that can influence the slurry supporting pressure in theory, comprises air pressure (Pa), slurry level (Hs), slurry feed rate (Qfs), slurry discharge rate (Qds), the different volumes between slurry discharging and feeding (Qdif), the volumes of shield excavating (Qexca), the slurry density of discharging (ρds), the slurry density of feeding (ρfs), advance speed (v), total thrust force (F), cutter revolutions (n) and torque (T). Then both the way and the extent that these variables contribute to the identifier's performance were analyzed with the in-situ data collected from a railway tunnel project to finally determine the identifier input features. The degree of cross-correlation between the candidate variables and the slurry supporting pressure was shown in Table 1, which was identified based on the normalized in-site data during shield tunneling. As it can be seen, the candidate feature set whose elements all have considerable relationship with respect to the slurry supporting pressure is {Pa, F, Qfs, ρds, Qds, ρfs, Hs, Qexca, Qdif, T}, while the advance speed and the cutter head revolutions are less relevant. This analysis result can be interpreted by the fact that the influence of advance speed on the air pressure and slurry level, which affect the slurry supporting pressure directly, is minor and negligible. In addition, to maintain the slurry pressure balance in shield tunneling, the operators scarcely regulate the advance speed and cutter head revolutions which mainly influence the quality of supporting slurry membranes and the performance of propulsion systems. So as a result, the advance speed and the cutter head revolutions were discarded from the candidate input features of slurry pressure identifier. After the correlation analysis, the redundant information of improved candidate features was eliminated using feature subset selection method in this study. Namely, through the training and testing based on the recorded data, it was found that both the exclusion and inclusion of the excavating volumes, slurry flow rate deviation and cutter head torque did not produce obvious influence on the performance of DRNNbased identifier. So as to relief the computational burden of control system, these three features were excluded. Then the pool of candidate input features was further evolved and comprised {Pa, F, Qfs, ρds, Qds, ρfs, Hs}. However, although the shield total thrust and the velocity and density of slurry flow all exhibited stronger relations to the slurry supporting pressure than slurry level, they either cannot affect the slurry supporting pressure independently or would be determined by other objectives instead of the target of slurry pressure balance. For instance, the total thrust mainly depends on the geological conditions and the diameter of shield machine. Furthermore, both the velocity and density of slurry flow are the operation parameters of slurry circulation system, and the essential of affecting the slurry pressure is through influencing the slurry level to interact with the air pressure holding system ultimately. It also can be seen from the Table 2 that the fluctuation of slurry level was mostly related to the density of slurry flow

S O j

(k)

u(k)

H ij

S

(k) D j

(k)

Fig. 4. Structure of diagonal recurrent neural network.

At each discrete time k, ui(k), i = 1, 2, ⋯, n is the i−th input feature. υj(k), j = 1, 2, ⋯, m is the sum of j−th hidden neuron's inputs and yjH(k), j = 1, 2, ⋯, m is its output. y(k) is the unique output of the DRNN model. In addition, the bias term of the output neuron is denoted as y0H(k) = 1, the bias term of the hidden neurons is represented as u0(k) = 1. According to the network structure, ωH, ωD and ωO represent the hidden, self-feedback and output connection coefficient matrix, respectively. For instance, ωijH is the hidden layer synaptic weight between i−th input node and j−th hidden neuron. Then the DRNN output can be derived m O H j (k ) y j

y (k ) =

(k )

(1)

j=0

yjH

(k ) = fsig ( j )

(2) n

j

=

D H j (k ) y j

(k

H ij

1) +

( k ) u i (k )

(3)

i=0 O

where fsig(υj) is the sigmoid function, ωj (k) is the output weight connecting the j−th hidden neuron and the output neuron, ωjD(k) is the selffeedback weight of j−th hidden neuron. Then we can see m

y (k ) =

O H 0 (k ) y0

n O j (k ) fsig

(k ) +

D H j (k ) y j

(k

H ij

1) +

j=1

(k ) ui (k )

i=0

(4) which presents a nonlinear time-varying neural network. Given the training set {u(k), d(k)}k=1N with N patterns, where d(k) is the real output value of k−th training data, the objective of training procedure is to obtain the optimum weight parameters ωH, ωD and ωO, so that the following cost function is minimizing.

J (k ) =

N

1 N

y (k )) 2

(d (k )

(5)

k=1

However, both the weight parameters and the topology structure of DRNN have the significant influence on the performance of slurry pressure prediction. Considering this practical problem, an evolved

Table 1 Correlation coefficients (Coe.) between the candidate input features and the slurry supporting pressure (Ps). Coe.

Pa

F

Qfs

ρds

Qds

ρfs

Hs

Qexca

Qdif

T

n

v

Ps

0.7029

0.6356

0.6202

0.4453

0.3735

0.2814

0.2563

0.2473

0.2309

0.2194

0.1755

0.0771

4

Automation in Construction 107 (2019) 102928

X. Li and G. Gong

Table 2 Correlation coefficients (Coe.) between the shield operation parameters and the slurry level (Hs). Coe.

ρds

F

Ps

Pa

ρfs

n

v

Qds

Qfs

Qexca

Qdif

T

Hs

0.3657

0.2631

0.2563

0.1791

0.1762

0.1105

0.1101

0.0830

0.0826

0.0798

0.0797

0.0442

and the air pressure. According to [3], let Paxe denotes the slurry pressure at the center of cutter head, Pair denotes the air pressure, ρni represents the density of mixed material in slurry chamber, g represents the acceleration of gravity, H and r represent the slurry level and radius of slurry shield respectively, then we can get the empirical formula

Paxe = Pair +

ni

g (H

i

w = wmax

ds (k ), fs (k ), Ps

1), Pa (k + p), Hs (k + p) )

i1

i2

vectors, and each element has a specified bound determined by the practical problems. The w is inertia weight within the interval [0, 1], the c1 and c2 are nonnegative constants of learning rate, the r1 and r2 are the random numbers uniformly distributed in [0, 1]. When the desired performance represented by gbest is achieved or the maximum generations are reached, the iteration of the algorithm could be terminated. To establish a better balance between the exploration and exploitation abilities of PSO method, the following annealing formulation of w from [50] was utilized in this study.

Ps (k + h) (k + h

(8)

where xk = (xk , xk , ⋯, xkiq), vki = (vki1, vki2, ⋯, vkiq), Pki = i1 i2 iq g g1 g2 gq (Pk , Pk , ⋯, Pk ) and Pk = (Pk , Pk , ⋯, Pk ) are all the q-dimensional

This formula also indicates that the slurry level is a major factor affecting the slurry supporting pressure. As a result, it is reasonable and feasible to select the air pressure and slurry level as the major control variables of the proposed MPC system for slurry pressure balance in shield tunneling. In view of the above discussion, combining with the locally recurrent property of DRNN model, the input features of slurry pressure predictor were finally determined and illustrated as follows.

= DRNN (Pa (k ), Hs (k ), Qfs (k ), Qds (k ), F (k ),

xki )

(9)

xki + 1 = xki + vki + 1

(6)

r)

xki ) + c2 r2 (Pkg

vki + 1 = w vki + c1 r1 (Pki

wmax wmin k kmax

(10)

where wmax and wmin are the upper and lower bounds of inertia weight, and selected as wmax = 0.7, wmin = 0.1 in this paper. The kmax is the maximum number of generations and the k represents the current generation.

(7)

While at time instant k, the Ps (k + h) is the predicted slurry supporting pressure over the prediction horizon h, the Ps(k + h − 1) is the monitored slurry supporting pressure in slurry chamber, the Pa(k + p) and Hs(k + p) are the control laws, namely air pressure and slurry level, where p is the control horizon and satisfies p ≤ h.

4.2. Evolved PSO Although various bio-inspired swarm intelligence algorithms have been widely applied into complex system identification and industry areas [51–54], both global optimum searching ability and convergence speed are the major criteria for evaluating the performance of these methods, and PSO is not an exception. However, when it comes to the multi-extremum problems, the whole swarm of PSO technique may be trapped in the local optimum and resulting in premature convergence. Of course, there are substantial PSO variants have been designed to improve this drawback. Chen et al. [55] used an aging leader and challengers to adaptively assign the leader of the swarm and attract the particles toward better positions. Garg [56] adopted the genetic algorithm to enhance the diversity of swarm after forming each generation in PSO iterations, which is inevitable to degenerate the convergence performance. Zhao et al. [50] proposed a different method to update the particle's position and velocity, which replaced the global best position term with more fittest individuals' information. Shi et al. [57] incorporated the cellular automata mechanism into the PSO velocity update rule to change the trajectories of individuals and avoid the local minimum. Alatas et al. [58] used chaotic maps for parameter adaptation in PSO method to intensify the global searching ability and escape the local extremum trap. Based on an incremental mutation rate, Coban et al. [59] utilized a mutation operator for both position and velocity parameters of each particle in every PSO iteration to avoid local optimum. Ge et al. [60] resorted to the average and variance information of fitness values to identify the premature state and the corresponding inactive particles which need to be stimulated after each PSO iteration, which would also aggravate the computational burden. Every PSO variant discussed above possesses the special ability for solving particular optimization problems, and there is no single method can optimize all numerical problems effectively. Equipped with this insight, we proposed an evolved PSO (EPSO) technique to solve the identifier and controller of MPC system for slurry pressure balance in this paper. Let l denote the number of generations of each epoch in EPSO iterations, f(Pkg) and fe respectively represent the global optimal value

4. Evolved particle swarm optimization algorithm Particle swarm optimization (PSO) developed by James Kennedy and Russell Eberhart [49] is a popular heuristic algorithm based on stochastic strategy, which was inspired by the social interaction behavior of birds flocking, fish schooling and other animal population. It has been an effective and efficient computation technique for optimizing complex nonlinear numerical problems. The swarm of PSO comprises an appropriate quantity of individuals, namely particles, and each of which represents a potential solution to the studied issues. In the process of optimizing, every particle flies around the pre-defined multidimensional search space to find the global optimal value of objective function. However, at every time instant, each particle's velocity and position are adjusted according to its own experience and the information obtained from the whole swarm, so that the best position assessed by the pre-defined fitness function would be encountered by the all individuals. Considering the global optimization ability, excellent convergence property and good practicability, this paper employed PSO algorithm to solve the optimization problems of the proposed MPC system, and attempted to modify the general PSO method for improving its ability to overcome the problem of premature convergence and evolve the structure of DRNN model synchronously. 4.1. General PSO For the time instant k, let xki and vki respectively denote the i−th particle's position vector and velocity vector in the q-dimensional search space. In addition, using Pki for representing the previous personal best position of the i−th particle and recorded as pbest, and adopting Pkg to indicate the previous global best position obtained from the all particles and called gbest. Then, at the time instant (k + 1), each particle's velocity vk+1i and position xk+1i can be updated according to the following formulas. 5

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X. Li and G. Gong

of fitness function at k−th iteration and the expected fitness value. Then define the gradient of the global optimal fitness value for T−th optimization epoch (from k−th iteration to (k + l)−th iteration) as the formula

(T) =

f (Pkg ) (f

(Pkg )

START Initialize the positions and velocities of swarm

f (Pkg+ l ) fe ) f

(Pkg )

Initialize the pbest and gbest of swarm

(11)

f(Pk+lg)

where represents the global optimal fitness value at the end of training epoch T, namely the (k + l)−th iteration. It is obvious that the indicator η(T), T = 1, 2, ⋯ is restricted into the interval [0, 1] and can exhibit the optimization power of the current swarm. If not only is the η(T) less than a given threshold determined by the operator, but the global optimum solution of fitness function is also not obtained, we can conclude two potential problems: the first indicates that the EPSO algorithm has been stuck in local minimum and the second implies that the structure of the DRNN model is not suitable for the practical problem. So the objectives of the proposed EPSO method consist of identifying the premature convergence to improve it and evolving the topological structure of DRNN model. In this paper, we defined the following discriminant to identify the premature convergence state.

(T)

T=0, k=0 T=T+1 l=0 l=l+1, k=k+1 Update the velocity and position of each particle Update the pbest gbest of the particles

If l==lmax

0

1+

k

(12)

i

f (Pki + l ) fe ) f (Pki )

f(Pki)

If (T) 0

NO

n+Y 2

4.3. EPSO-based DRNN identifier

xi =

Generate evolved swarm of EPSO

k max

Report optimal solutions obtained from the EPSO END

Fig. 5. The evolved particle swarm optimization algorithm.

m

(n + Y ) + 10

(15)

where the m represents the number of hidden neurons. During the EPSO implementation, the mutation operator would modify the connections and structure of DRNN model. Therefore, in order to maintain the search space invariant, the dimensionality of particles in swarm is determined based on the maximum number of hidden neurons, mmax = (n + Y) + 10. Namely, the i−th particle can be illustrated as follows.

According to the principle of slurry pressure prediction and the feature analysis discussed in Section 3, we re-present the DRNN identifier for slurry supporting system as follows.

D| mmax × 1 , D

H

(n mmax + mmax ) × 1,

O

(mmax Y + Y ) × 1

(16)

where the ω |mmax×1 is self-feedback coefficient vector with mmax elements, the ωH|(n∙mmax+mmax)×1 is synaptic weight vector of hidden layer with (n ∙ mmax + mmax) elements (including the connection with bias term), and the ωO|(mmax∙Y+Y)×1 is connection weight vector of output layer with (mmax ∙ Y + Y) elements (including the connection with bias term). So it is obvious that each particle is equivalent to a ((n + 2 + Y) ∙ mmax + Y) × 1 vector. Considering the training procedure of EPSO shown in Fig. 5, and to avoid impairing the mapping abilities of DRNN model in the nonlinear dynamic processes, the self-feedback coefficient of any existing hidden neuron cannot be set to zero during the mutation. In addition, according to [62], we specify the mutation operator of the EPSO method based on a stochastic mutation probability ξ as follows. (1) If the number of hidden neurons satisfies m ≤ mmax, on the one

Ps (k + h) 1), Pa (k + p), Hs (k + p) )

f e or

Remain the surplus particles

YES

where the and represent the fitness value of i_th particle at k_th iteration and (k + l)_th iteration, respectively. The β0 is a userdetermined constant. Finally, the mutation operator is imposed on the chosen individuals to improve their searching abilities. The specific implementing measures of the mutation operator include deleting or adding connections among existing neurons and eliminating or attaching hidden neurons. When a new connection or hidden neuron is added to the DRNN model, the synaptic weights are randomly initialized according to the limits of search space. After the periodic supervision and mutation operator, not only the convergence speed and precision but also the optimization power and diversity of the swarm are heightened. Then it is time for the next EPSO optimization epoch and executing iteratively until the algorithm converges or the maximum generations are reached. The flowchart of the proposed EPSO algorithm is illustrated in Fig. 5.

(k + h

NO i

YES

Impose mutation operator to evolve selected particles

g If f( Pk )

(13)

If

)

NO

f(Pk+li)

= DRNN (Pa (k ), Hs (k ), Qfs (k ), Qds (k ), F (k ),

k

/(1

k

0

YES

YES

where η0 and τ are the user-selected constants. If the indicator η(T) does not satisfy the discriminant, the EPSO algorithm successfully avoids the pitfall of local minimum and has a good performance. It is also necessary to continue the next epoch in EPSO iterations according to update rules Eqs. (8)-(9). Otherwise, we use the following criterion to choose the trapped particles.

f (Pki ) = (f (Pki )

NO

ds (k ), fs (k ), Ps

(14)

Combining with the network shown in Fig. 4, we know the number of input nodes ui(k), i = 1, 2, ⋯, n of DRNN model is n = 10, and the output y(k) is unique. Let Y denote the number of network outputs, namely Y = 1 in this paper. Then the ideal number of hidden neurons based on the golden section principle [61] can be selected in the range determined by the following criterion. 6

Automation in Construction 107 (2019) 102928

X. Li and G. Gong

hand, the added neurons'number is (mmax − m) ∙ ξ, and randomly initialize their synaptic weights in the specified ranges. On the other hand, the deleted neurons'number is m ∙ ξ and set their synaptic weights to zero. 2) If the connected number excluding self-feedback and bias term is (n + Y) ∙ m, then the eliminated connections'number is [(n + Y) ∙ m] ∙ ξ and set their weights to zero. Identically, the attached connections'number is [(n + Y) ∙ (mmax − m)] ∙ ξ and randomly initialize their weights within the feasible domain, where the (n + Y) ∙ (mmax − m) is un-connected number excluding self-feedback and bias term in this study.

horizons on the fitness function of optimizer. Similarly, the penalty factor βj can not only penalize the excessive movement of the control variables, but also assess the hierarchical importance of the optimal multi-step ahead control laws. The Pao(k) and Hso(k) are the optimal control laws produced by the MPC system at time instant k. Therefore, the optimization model of the DRNN based predictive controller can be represented as follows.

min Pa (j), Hs (j) J (k + 1), j = k + 1, k + 2, k + 3

(21)

Subject to

5. DRNN and EPSO based slurry pressure control

Pa

As the model predictive control system shown in Fig. 3, the established predictive controller, taking slurry level and air pressure as primary control variables, is solved by the EPSO algorithm. Its objective is to provide the optimal control laws for slurry circulation system and air pressure holding system based on the multi-step ahead predictive slurry supporting pressure, so as to achieve the accurate tracking of the desired water-earth pressure and effectively compensate the long-term delays of slurry pressure regulation system. Namely, according to the time-variant geological conditions and operation parameters, the presented control model can produce the optimal reference online for the actuator systems to keep the tunneling face stability, which is obviously more reliable and superior than the conventional manual operations that mainly depends on the engineering experience.

min

Hs min

Pa (j) Hs (j)

Pa max Hs max

(22) (23)

where Pa min and Pa max denote the minimum and maximum values of air pressure respectively. Hs min and Hs max are the extreme values of slurry level. Through solving the above optimization problem via EPSO algorithm, we can obtain the optimal control laws for three steps ahead and only the immediately following one are used for the system regulation. 5.2. EPSO for the predictive controller In order to solve the nonconvex and inequality constrained optimization problem presented above, the proposed EPSO algorithm is slightly modified to derive the tuning rules of control variables and take into account the logical control sequence of the actuator systems simultaneously. Firstly, as the structure evolution is no longer involved in this optimization problem, the mutation operator of EPSO method degenerates to randomly mutating 6 ∙ ξ (regulate slurry level and air pressure concurrently) or 3 ∙ ξ (only regulate air pressure) elements of the selected particles according to the specified ranges. When the particle flies out of the limited search space, the algorithm directly sets its elements to the random values within the permitted region of control variables. We present the corresponding particle structure of this issue as follows.

5.1. DRNN based predictive controller In the DRNN based model predictive control system, the trained DRNN identifier is used to predict the slurry supporting pressure over h steps which will be selected as h = 3 in this paper. In the forecasting procedure of controller, the current predicted value is used as the input of the next prediction step to substitute the inaccessible actual slurry supporting pressure for the next step. With respect to the multi-step ahead prediction, this iterative approach is more stable than the forecasting process using multiple different predictors [63]. Let the control horizon p = 3, then the DRNN predictors can be illustrated as follows.

x i = [Pa (k + 1), Pa (k + 2), Pa (k + 3), Hs (k + 1), Hs (k + 2), Hs (k + 3)] (24)

Ps (k + 1) = DRNN (Pa (k ), Hs (k ), Qfs (k ), Qds (k ), F (k ),

Secondly, because of the slow response of slurry level regulation, when the fluctuation of slurry level is in the acceptable range, the slurry pressure stabilization is mainly depended on the air pressure reconfigurations. On the other hand, when the changes of slurry level exceed the permitted range and result in slurry pressure uncontrollable only through the air pressure holding system, it is necessary to adjust the slurry level by feeding or discharging slurry firstly and regulate the air pressure as an auxiliary method. Incorporating this knowledge into the EPSO programing for predictive controller, we can illustrate the training procedure as follows. (1) When the actual slurry level at time instant k, Hs(k) is maintained in the range of [Hs low, Hs up], where the Hs low and Hs up are the acceptable bounds of slurry level, we let

ds (k ), fs (k ), Ps (k ), Pa

(17)

(k + 1), Hs (k + 1) )

Ps (k + 2) = DRNN (Pa (k ), Hs (k ), Qfs (k ), Qds (k ), F (k ),

ds (k ), fs (k ), Ps

(k + 1), Pa (18)

(k + 2), Hs (k + 2) ) Ps (k + 3) = DRNN (Pa (k ), Hs (k ), Qfs (k ), Qds (k ), F (k ),

ds (k ), fs (k ), Ps

(k + 2), Pa (19)

(k + 3), Hs (k + 3) )

After that, the predicted slurry supporting pressure is transmitted to the optimizer of the predictive controller. Then, the optimal values of slurry level and air pressure for the further regulations are obtained by minimizing the errors between the desired water-earth pressure (Pd) and the predicted values over the prediction horizons. Considering the prediction uncertainties and the gradient limits of control variables, the cost function of optimizer is designed and formulated as k+3

J (k + 1) =

Hs (k + 1) = Hs (k + 2) = Hs (k + 3) = Hso (k )

where Hso(k) is the optimal slurry level solved by EPSO at time instant k. Then we only need to update the first three elements of each particle using EPSO method. (2) When the Hs(k) is beyond the range of [Hs low, Hs up], we update all elements of particles using EPSO method. The manipulation procedure of shield tunneling based on the proposed MPC system for slurry pressure balance is illustrated in the Fig. 6. It is obvious that the time delays in the slurry pressure balance control system can be effectively inhibited through the logical optimization of controller and the advanced predictions from the identifier. In addition, there is an important detail must be perceived during the slurry shield tunneling. That is when the slurry level exceeds the pre-determined

k+3 i

|Pd (i )

(Ps (i )

i=k+1

(|Pa (j)

P (k ))| + j=k+1

Pao (k )| + |Hs (j)

Hso (k )|)

(25)

j

(20)

Here, P (k ) = Ps (k ) Ps (k ) is the prediction error at the time instant k. The αi is the penalty factor belonging to the interval [0, 1] which can evaluate the influence of predictors with different prediction 7

Automation in Construction 107 (2019) 102928

X. Li and G. Gong

START

Set the desired water-earth pressure

Monitor slurry shield operation parameters

Establish optimizer Update the

min P (j),H (j) J(k 1) a

s

training set

If H s low H s (k)

YES

Set H s (k 1) H s (k

H s up

Solve Pa (k 1), Pa (k Update the

2)

H s (k 3) H so (k) Pa (k

NO

2)

) using EPSO

DRNN model based on EPSO

Solve H s (k H s (k

and Pa (k

Predict the slurry pressure for three

1), H s (k

3), Pa (k

2)

3) using EPSO

Transmit H s (k Pa (k

2)

1), Pa (k

1) and

1) to actuator systems

steps ahead If H s min H s (k)

YES H s max

Regulate slurry level and air pressure

ADVANCE

NO STOP Fig. 6. The manipulation flowchart of slurry pressure balance control in shield tunneling.

security scope, we must stop the construction until operation conditions return to the normal through some remedial measures.

using slurry-type tunnel boring machine (TBM) through two-way construction and supported by the tunnel segments with inner diameter 9.5 m. The slurry shield used for the tunneling section I was provided by China Railway Engineering Group CO., LTD and its specifications were described in Table 3. The whole tunnel is located in alluvial plain without either large slope or seismic and geological hazards caused by rock mass collapse, cracking and landslide. While, the problems of ground deformation and hidden fault were encountered unfortunately. Situated in downtown area, there are many important buildings, intricate highways, subways and municipal pipelines along the tunnel. According to the geological survey, there is also a hidden fault through the vicinity of the tunnel section from DK21 + 788 to DK21 + 802, and the average annual ground subsidence around the fault was about 50 mm in recent years. So in order to accurately curb the ground deformation, it is significant and imperative to achieve the slurry pressure balance effectively in shield tunneling, and enhancing the supporting structure of the tunnel is also very important. The geological compositional data show that the strata penetrated by the tunneling section I mainly consists of 45% silty clay, 32% silty sand, 18% silt and 5% clay. The tunnel section I intersects with the North Creek at DK19 + 670-DK19 + 700 and the average annual precipitation of the district was generally between 550 mm and 650 mm.

6. Simulation and discussion The simulation results presented in this section are customized for the construction of an intermediate section of Wangjing railway tunnel, which is an important connection segment of the railway passenger dedicated line from Beijing to Shenyang in China. In order to demonstrate the superiority of the EPSO-based DRNN model and MPC system for the slurry pressure balance control with complex uncertainties and time delays, both the standard particle swarm optimization method (PSO) and the genetic algorithm (GA) were employed to optimize the DRNN identifier and predictive controller for a comparison. The dynamic back-propagation algorithm (DBP) was also used for training the DRNN model as a contrast. 6.1. Tunneling project and in-site data Considering the special construction environment and the complex geological conditions, as shown in Fig. 7, Wangjing railway tunnel located between the South Road of Caochangdi (DK18 + 550) and the south of Qinghe Town (DK26 + 550) in Beijing was mainly constructed 8

Automation in Construction 107 (2019) 102928

X. Li and G. Gong

Section 2# Shield Shaft TBM Outlet

Shenyang

DK26+550

DK25+910

DK22+710

Slurry-type TBM

DK22+690

DK18+990

Slurry-type TBM

DK19+010

DK18+550

Beijing

3# Shield Shaft TBM Inlet

DK25+890

1# Shield Shaft TBM Inlet

Section

Fig. 7. The construction layout of Wangjing railway tunnel. Table 3 The specifications of the experimental slurry shield. Item

Parameters

Value

Shield

Type of driving Open ratio of cutter face Driving power Excavation diameter Shield diameter Rated torque Breakout torque Revolutions Rated revolutions Maximum advance speed Number of jacks Total thrust Feeding pipe diameter Discharging pipe diameter Designed slurry feed rate Designed slurry discharging rate

Electric 45% 2240KW 10.88 m 10.85 m 31000KN ∙ m 38750KN ∙ m 0–2.0 rpm 0.8 rpm 30 mm/min 50 12,380 T 450 mm 450 mm 1860m3/h 2140m3/h

Shield jacks Slurry circulation

More than 80% of annual precipitation was also concentrated in the flood season, so waterlogging may be encountered in low-lying areas even for drought years. Besides, the buried depth of tunnel is 16.1 m–34.3 m and the maximum water-earth pressure of tunnel center is 4.36 bar. Briefly, both abundant groundwater and surrounding rock with poor self-stability can affect the excavating face stability considerably. Not only must the slurry pressure balance control system be robust to the complex construction conditions, but strengthening the monitoring of the deformation extent for the major buildings on the ground is also crucial. To obtain the diversified data sets with changeable geology and confirm the advantages of the proposed method effectively, the simulation data were collected from the segment ring 151 to ring 350 of the tunneling section I, which width of each segment ring was 2 m. The sampling frequency of the data acquisition system was 0.1 Hz. The actual slurry supporting pressure was monitored by four sensors located on the bulkhead and their particular locations were illustrated in Fig. 8. We selected the monitoring value of sensor I as the actual slurry supporting pressure in the simulation experiments, which is closest to the tunnel center and located 5 m horizontally and 0.4 m vertically apart from the axes respectively. However, the quality of data is crucial to ensure and enhance the MPC performance. So in order to improve the completeness and representativeness of the collected data, based on the slurry shield tunneling mechanism, we first defined a discriminant index as

D = d (v ) d (n) d (Qds ) d (Qfs )

Fig. 8. Locations of slurry pressure sensors on the bulkhead.

It is obvious that the slurry shield machine is on the construction if and only if D ≠ 0. So the discriminant index D was employed to eliminate the garbage in the acquired measurement data during the time of shut down. Furthermore, the outliers of data sets caused by start-stop conditions and uncertainties were removed using the statistical analysis method, namely the data sets with unreasonable advance speed and slurry discharge rate were discarded. Then we divided each segment ring into 10 equal sections and the evolved simulation data for each section were averaged. Finally, for the 200 segment rings, there were 2000 sets of the average data to be used for implementing the simulation experiments. Furthermore, to ensure the effectiveness and robustness of the predictive controller, it is necessary to forecast the slurry supporting pressure accurately and evolve the DRNN model online using the EPSO method. Equipped with this insight and using the systematic sampling method, the preprocessed data were divided into training subset and testing subset in the ratio of 3:1 to train and evaluate the DRNN identifier for slurry pressure, namely composed of 1500 patterns and 500 patterns respectively. Then the trained DRNN model was provided to confirm the superiority of the MPC method for the dynamic slurry pressure balance control, based on the same data sets where the tunneling stratum is changeable. In the process of slurry shield tunneling, the desired water-earth pressure usually can be derived from the active and passive soil pressure, which are calculated based on Rankine's theory according to the surveyed geological and hydrological conditions. Based on this insight

(26)

where the variable set {v, n, Qds, Qfs} can effectively describe the operating status of shield machine in real time. The function d(x) satisfies

d (x ) =

1, if x 0 0, if x = 0

(27) 9

Automation in Construction 107 (2019) 102928

X. Li and G. Gong

Table 4 Performance of EPSO-based DRNN with different major factor values on the training data. RRMSE ×10−2

Num

and the collected in-situ data, we can evaluate the performance of the manual control scheme for slurry pressure balance during construction. As shown in Fig. 9, the actual slurry supporting pressure cannot track the expected water-earth pressure effectively, and the former obviously lags behind the latter, especially encountering the rapid changes of the geological conditions. This comparison result also evidently exposes the weakness and limitations of the manual operations and at the same time, it is worthy to improve the accuracy and intelligence of slurry supporting pressure control system. 6.2. Performance of identification In this section, the presented DRNN predictor was established according to Eq. (14) and the root mean square error (RMSE) was employed as the cost function, namely

1 N

N

i

(P s i=1

Psi ) 2

20 30 50 70 100 150 200 250

5

10

15

20

25

4.024 2.146 1.021 1.231 1.069 0.752 0.877 0.776

2.680 2.417 1.737 1.104 0.771 0.807 0.793 0.544

2.820 1.273 1.996 1.528 1.008 0.786 1.002 0.778

2.326 1.827 1.423 0.707 0.877 0.789 0.816 0.636

4.822 2.218 1.879 1.209 1.124 0.875 0.898 0.684

effectively inhibited. For another, when the swarm approaches the global optimum, namely the stable state, the more generations for each epoch are able to prevent the mutation operator from inducing the particle to jump out of the optimal location, and also can accelerate the convergence. Therefore, taking into account the prediction accuracy of DRNN and the time consumption of control system, the parameters were determined l = 10, Num = 100. Based on the derived EPSO-DRNN model, the slurry pressure predictors, described by Eqs. (17)–(19), were easily established. The changeable geology also has a significant function to test the capability of the presented model that producing the multi-step ahead predictions. Furthermore, as one of the prevailing swarm intelligence algorithms, the GA method possesses mutation operator which also exists in the presented EPSO. Based on the conventional gradient method, the DBP algorithm was widely used for updating the parameters of dynamic neural networks. So in order to illustrate the advantages of the proposed EPSO algorithm, the standard PSO method, the popular GA program and the classic DBP algorithm were all employed to train the DRNN model described by Eq. (17) on the training data for comparison. Unlike the population-based optimization algorithms, adjustments to the synaptic weights of DRNN by DBP method are performed according to the partial derivative terms of objective function. So the cost function of DBP learning was defined by the mean square error (MSE) in this paper, namely

Fig. 9. Comparison of the monitored slurry supporting pressure and the expected water-earth pressure.

J=

l

(28)

where the N is the number of training data groups and N = 1500 for i this case, the P s is the predicted slurry pressure based on i_th data group, and the Psi is the actual one. Besides, the synaptic weights and structure of DRNN model were evolved automatically using the suggested EPSO method in Section 4. As the training procedure shown in Fig. 5, we selected the initial number of hidden neurons as m = 15 and randomly initialized the corresponding elements of each particle in the range [−1, 1]. Through many testing and comparison, the most appropriate parameters for the EPSO method in this case were determined as: the expected fitness value fe = 10−6, the inertia weight wmax = 0.7 and wmin = 0.1, the maximum iterations kmax = 300, the learning rate c1 = c2 = 1.5, the gradient parameters η0 = 0.6, τ = 5 and β0 = 0.2, the mutation probability ξ = 0.1, the initial connected number (n + Y) ∙ m = 165. In addition, both the number of generations (l) for each optimization epoch and the swarm size (Num) are the major factors that influence the performance of EPSO method for preventing premature convergence and improving global optimum searching ability. Considering the forecasting accuracy, we evaluated the performance of the prediction model based on the relative root mean square error (RRMSE) with different major factor values of the EPSO. As the results cited in the Table 4, both the larger and smaller value of l had better contributions to the forecasting performance of the DRNN model. It can be interpreted as follows: for one thing, the fewer the generations for each epoch, the more frequently implementing the mutation operator and as a result, the premature convergence of EPSO algorithm can be

JDBP =

1 2N

N

i

(P s i=1

Psi ) 2

(29)

To avoid the influence of uncertainties on the comparison results, the basic parameters of these three algorithms were selected in consistent with the EPSO and the number of hidden neurons of corresponding DRNN model was also set to 21, the same number of the maximum ones of EPSO-based DRNN model. More details about the optimal parameters and performance of the algorithms were illustrated in the Table 5. On the testing data, the mean absolute error (MEAE) of EPSO-DRNN was superior to PSO-DRNN, GA-DRNN and DBP-DRNN by 0.85%, 3.65% and 2.17%, respectively. The maximum absolute error (MAAE) of the testing samples also showed that the EPSO method was more precise and robust than the others for slurry pressure identification. Under the above conditions, the best performance achieved by each algorithm was shown in Fig. 10 and Fig. 11. It can be seen from the Fig. 10 that the EPSO method consistently performed better prediction accuracy compared to the other three algorithms. Particularly, the EPSO-DRNN model can adapt to the changes of geological conditions rapidly and track the actual slurry supporting pressure accurately. Nevertheless, the PSO and DBP cannot evolve the structure of DRNN model timely to accommodate the geological changes and lead to greater prediction error on some specific points. As depicted in Fig. 11, the EPSO algorithm also obviously outperforms the other methods in convergence speed. The GA with slowest convergence rate exhibited worst forecasting performance. Therefore, the training 10

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X. Li and G. Gong

Table 5 Optimal parameters and performance of EPSO, PSO, GA and DBP on the DRNN predictor training. Model

Parameters

EPSO PSO GA DBP

MEAE (%)

MAAE (%)

Objective function

Maximum iterations

Swarm size

Learning rate

Train

Test

Train

Test

RMSE RMSE RMSE MSE

300 300 300 300

100 100 100 –

[0.1, 0.7] [0.1, 0.7] – [0.1, 0.4]

0.5540 1.4722 3.9910 2.6988

0.6230 1.4682 4.2755 2.7943

5.5568 13.3230 20.6696 13.1308

6.9928 14.0490 27.9850 14.3412

automatically. Then the trained identification model was employed to establish the controller of MPC system for slurry pressure balance.

0.5 GA DBP PSO EPSO

0.4 0.3

6.3. Performance of MPC

0.2

According to the manipulation procedure shown in Fig. 6, it is obvious that the DRNN-based identifier is the basis for the controller which produces the optimal regulation laws for the slurry circulation system and air pressure holding system. The EPSO method was used to solve the optimization model complying with the limits of slurry level and air pressure, taking into account the logical control sequence of actuator systems illustrated in Section 5, simultaneously. Based on the multi-step ahead predictions, the optimizer of MPC system was established according to Eqs. (20)–(23), and the reference of control variables was derived by minimizing the deviation between the predicted slurry supporting pressure and the desired one. In order to justify the superiority of the DRNN and EPSO based MPC system for slurry pressure balance control, the relevant parameters were selected: the maximum slurry level Hs max = 1.2m, the minimum one Hs min = − 2.4m, the predefined acceptable range of slurry level Hs up = 0.5m and Hs low = − 0.6m, all of which were relative to the central line of the air chamber, the feasible region of air pressure Pa min = 1.5bar and Pa max = 4.36bar. According to the customized EPSO method proposed in Section 5, many experiments and analysis had been carried out to seek the optimal value of fitness function Eq. (20) for each sample, then the implementing conditions of EPSO were determined: fe = 10−6, αk+1 = 1, βk+1 = βk+2 = βk+3 = 0.01, wmax = 0.7, αk+2 = αk+3 = 0.1, wmin = 0.1, kmax = 200, c1 = c2 = 1.5, η0 = 0.6, τ = 5, β0 = 0.2, ξ = 1, l = 10, Num = 100. In order to validate the advantages of the EPSO algorithm, both the PSO and GA methods were applied to solving the same optimization model for the MPC system and establishing a fair comparison basis by using identical basic parameters with EPSO. The optimal control laws, namely the slurry level and air pressure, produced by EPSO, PSO and GA were illustrated in Fig. 13, Fig. 14 and Fig. 15, respectively. During the construction of part I, the monitored slurry level mostly exceeded the acceptable range [Hs low, Hs up], so the slurry level was mainly regulated to maintain the slurry supporting pressure and adjusting the air pressure supplementarily. When it comes to part II with mutant geology, it was necessary to regulate both the slurry level and air pressure concurrently to keep the excavating face stability timely. However, in the tunneling process of part III, the actual slurry level was in the acceptable range and the slurry pressure stabilization was primarily depended on the air pressure regulating. As the simulation results depicted in Fig. 13, it can be concluded that the presented EPSO algorithm for the predictive controller of MPC system can effectively produce the optimal control laws with gradual changes for slurry circulation and air pressure holding systems, considering the logical control sequence discussed in Section 5. Nevertheless, as the experimental results shown in Fig. 14 and Fig. 15, the control laws solved by PSO and GA methods all showed randomly intense fluctuation and mutable process. Moreover, the reference of slurry level and air pressure provided by GA exhibited rapidest changes, which were not suitable for the control of actuator systems.

0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 0

500

1000

1500

Training sample sequence

Fitness value (RMSEx10 -2 )

Fig. 10. Comparison of prediction error between EPSO and other algorithms.

Fig. 11. Comparison of updating process between EPSO and other algorithms.

results indicate that the EPSO algorithm has a considerable improvement in searching the global optimum and optimizing the DRNN structure than PSO, DBP and GA methods. To justify the effectiveness of the proposed predictors, the testing data were used to test the trained DRNN model and the forecasting performance is depicted in the Fig. 12. Owing to the versatile evolving procedure of EPSO algorithm and the nonlinear time-variant mapping ability of DRNN model, the forecasted slurry pressure can consistently conform to the actual values, and the predictor was robust to the rapid changes of the predictive targets. According to mean absolute error criterion, the forecasting results for predictive horizon of 1 step outperformed the results for predictive horizon of 2 steps and 3 steps by 0.56% and 0.99% on the testing data, respectively. Based on the training data and testing data, both the simulation results and analysis discussed above demonstrated that the EPSO-DRNN model can forecast the slurry pressure accurately and adapt to the geological changes 11

Automation in Construction 107 (2019) 102928

X. Li and G. Gong

Fig. 12. Slurry pressure forecasting results for predictive horizon of 1 step, 2 steps and 3 steps using the EPSO-DRNN model on the testing data.

Based on the best control laws provided by the proposed MPC system, the control performance for slurry pressure balance is shown in Fig. 16. Obviously, the slurry supporting pressure produced by the DRNN and EPSO based MPC system can track the expected water-earth pressure accurately and adapt to the geological changes effectively. Compared to the manual operation results shown in Fig. 9, an improvement of 5.11% and 13.58% was achieved by the approach presented in this paper, respectively for the mean absolute error (MEAE) and the maximum absolute error (MAAE). Furthermore, the problem of hysteresis was improved prominently, especially for the regions with mutable geological conditions. It is also transparent that both the PSO and GA exhibited inferior performance compared with the EPSO, which was superior to the PSO by 0.57% and 5.07%, and outperformed the GA by 1.48% and 31.00%, respectively for the MEAE and MAAE. As can be seen from the experimental results and theoretical analysis, the proposed EPSO method was proved with several evident superiorities in both numerical optimization and engineering application. Firstly, compared with existing anti-premature PSO variants, the EPSO can effectively improve premature convergence with less computational

burden by performing mutation operator on selected trapped particles only at the end of each evolution period during iterations, and the impact of evolution period on the EPSO performance was ascertained. Then, the comparison results also demonstrated that the EPSO with periodic supervision and mutation possesses superior global optimum searching ability and higher convergence speed than other well-known algorithms, such as standard PSO, GA and DBP. At last, the EPSO method customized for DRNN updating and slurry pressure regulation can better cater to the changeable stratum and confront time delays than the other algorithms. From the simulation results and discussion in this section, it can be concluded that the presented control strategy in this paper can keep the slurry pressure balance effectively and enhance the robustness of control systems significantly. To stabilize the excavating face during slurry shield tunneling, it is crucial for the control systems to automatically adapt to the complex geology and timely provide applicable control laws. So both the robust tracking performance and versatile online updating abilities from the proposed model are important and imperative for shield construction, which considering the problems of

Fig. 13. The optimal slurry level and air pressure obtained from the DRNN and EPSO based MPC system. 12

Automation in Construction 107 (2019) 102928

Pa

Hs

(m)

(Bar)

X. Li and G. Gong

Fig. 14. The optimal slurry level and air pressure obtained from the DRNN and PSO based MPC system.

inaccuracy and hysteresis excellently. Compared with the manual operations and previous researches, the major benefits from the model application includes improving time delays of slurry pressure regulation, producing more practicable control laws and tracking the expected water-earth pressure more precisely and robustly. For the MPC system, the monitoring slurry pressure from the sensor I, which is closest to the tunnel center among the decentralized measurement sensors on the bulkhead, was used as the identification target, namely which was regarded as the actual slurry supporting pressure in this paper. However, the slurry chamber is a complex multiphase flow system and the actual supporting pressure is nonlinear and timevarying. So the validity of the chosen prediction target is needed to be confirmed by applying the model in shield tunnel engineering practice. How to accurately ascertain the actual slurry supporting pressure can also be further considered, so that the practical balance with the desired water-earth pressure is able to be established and the more appropriate prediction and optimization targets for the proposed MPC method can be obtained. Besides, the operation parameters of slurry circulation and

air pressure holding systems not only are responsible for tunneling face stability, but also determine the slurry pipe abrasion and the compressed air absorbility of pressure impact and pressure fluctuation caused by shield tunneling and changeable operation conditions. Thus the further researches could take the coordination controls into consideration combining the slurry pressure balance and the above discussed factors. 7. Conclusion In order to improve the disadvantages of manual operations in shield tunneling, a model predictive control (MPC) system for slurry pressure balance was proposed in this paper. A diagonal recurrent neural network (DRNN) was employed to provide multi-step ahead forecasts of the slurry supporting pressure based on the main factors selected by feature analysis. An evolved particle swarm optimization (EPSO) algorithm, which adopted periodic supervision and mutation to foster convergence speed and precision, was presented to update the

6

2 Air pressure reference P ao solved by GA Slurry level reference H so solved by GA

4 0

2

-2

Mainly Regulate Hs and supplementarily adjust Pa

Mutant geology

Regulate P a mainly

0 0

200

400

600

800

1000

1200

1400

1600

1800

Sample sequence Fig. 15. The optimal slurry level and air pressure obtained from the DRNN and GA based MPC system. 13

2000

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Slurry supporting pressure (Bar)

X. Li and G. Gong

Fig. 16. Comparison of control performance among the GA, PSO and EPSO based MPC system.

synaptic weights and structure of DRNN model concurrently. Then, based on the predicted slurry pressure over three prediction horizons, the predictive controller was established by minimizing the deviation between the desired water-earth pressure and the forecasted one. The proposed EPSO method was used to solve the optimization model of the controller to produce the optimal slurry level and air pressure, taking into account the logical control sequence between the slurry circulation system and the air pressure holding system. Based on the in-situ data collected from Wangjing railway tunnel project in China, the simulation results demonstrated that the DRNN and EPSO based MPC system can accurately track the expected slurry supporting pressure and effectively adapt to the geological changes. Furthermore, both the standard particle swarm optimization method and the genetic algorithm were applied to training the DRNN identifier and solve the optimization model for comparison. The dynamic back-propagation algorithm was also used for DRNN updating. The contrast results indicated that the proposed EPSO method has superior optimization ability, higher convergence speed and stronger robustness to changeable targets.

[3] [4] [5]

[6] [7]

[8] [9]

Acknowledgement

[10]

This work was supported by the National Basic Research Program of China [973 Program; grant numbers 2015CB058100, 2015CB058103]; the National Natural Science Foundation of China [grant number 51675472]; the Henan Province Major Science and Technology Projects, China [grant number 161100211100]; and the National Key Research and Development Program of China [grant number 2017YFB1302602].

[11] [12] [13]

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[14]

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