In order to solve the problems of strong coupling, nonlinearity, and complex mechanism in real-world engineering process, building soft sensor with excellent performance and robustness has become the core issue in industrial processes. In this paper, we propose a new soft sensor model based on improved Elman neural network (Elman NN) and introduce variable data preprocessing method to the soft sensor model. The improved Elman NN employs local feedback and feedforward network mechanism through context layer to accurately reflect the dynamic characteristics of the soft sensor model, which has the superiority to approximate delay systems and adaption of time-varying characteristics. The proposed variable data preprocessing method adopts combining Isometric Mapping (ISOMAP) with local linear embedding (LLE), which effectively maintains the neighborhood structure and the global mutual distance of dataset to remove the noises and data redundancy. The soft sensor model based on improved Elman NN with variable data preprocessing method by combining ISOMAP and LLE is applied in practical sintering and pelletizing to estimate the temperature in the rotary kiln calcining process. Comparing several conventional soft sensor model methods, the results indicate that the proposed method has more excellent generalization performance and robustness. Its model prediction accuracy and anti-interference ability have been improved, which provide an effective and promising method for the industrial process application.

Soft sensor is an inferential prediction virtual technique which adopts easily measured variables to predict the process variables which are difficult to measure directly because of technological and economical limitations or complex environment. The soft sensor tries to establish a regression prediction model between easily measured variables and difficultly measured variables, which is adopted to solve the problem that prevents the measurements from being employed as feedback signals for quality control systems. And the soft sensor methods have been employed more widely in the industrial process and become a major developing trend in both academia and industry [

In view of the model prediction in the industrial production process, early scholars put forward some model predictive control, such as generalized predictive control [

However, the complexity of the industrial model will increase and bring about the problem of dimensionality with variables increasing. In addition, there are strong correlations and considerable redundancy between variable data. And the collected variable data may be contaminated by random noises or abnormal working condition data, which indicates that the process variables for soft sensor are stochastic. If those variable data samples are used directly for establishing the soft sensor model, the performance of the soft sensor model may not be guaranteed, which results in terrible prediction accuracy or poor estimation. Hence, it is significant to discover the general trends of data by latent variable models before soft sensor modeling. And the randomness of variable sample data should be taken into consideration and the redundant variable sample data need to be discarded selectively through the use of appropriate variable selection techniques. The core is to exploit the essential information behind the effective sample data to establish a soft sensor model that has excellent performance and strong robustness. The shortcoming of variable sample data has advanced the development of the dimension reduction methods. So many data preprocessing methods for the soft sensor model have been researched in recent years. Sun et al. [

The rest of this paper is organized as follows. Section

For convenience, some definitions that will be used throughout this paper are given: NN: neural network; ISOMAP: Isometric Mapping; LLE: local linear embedding.

Elman neural network (Elman NN) [

To further improve the dynamic performance and nonlinear approximation capability of Elman NN, the output of context layer as a feedback signal should be fully taken advantage of. Figure

Architecture of improved Elman NN.

From Figure

Structure block diagram of improved Elman NN.

We define the following symbols: the number of input layer nodes, output layer nodes, and hidden layer nodes is

The mathematical model in which the input layer is mapped to the hidden layer through the mapping activation function is

The hidden layer

Equation (

In the training process, the output of the context layer

The loss function is defined as the squared error:

A novel set of parameter vector of the improved Elman NN can be obtained and optimized to minimize the expected average squared error:

Considering the original input variables of improved Elman NN exist with redundant variable data and abnormal condition variable data, a novel variable data selection methodology by integrating Isometric Mapping (ISOMAP) [

The general steps of the data dimensionality reduction process are the following.

Use

Use the shortest path method to calculate the geodesic distance

The matrix expression is constructed according to the matrix

Obtain the maximum eigenvalue

In order to ensure that

For each data point of the LLE algorithm

The weight coefficient

Obtain the kernel matrix of

Calculate the eigenvalue matrix

Soft sensor model based on improved Elman NN with variable data selection is aimed at exploiting the essential information behind the process data and filter redundant variable data in the soft sensor model. This paper proposes an input variable data selection and dimension-reduction methodology by integrating ISOMAP and LLE manifold learning algorithm, which is effective to solve redundant variable data and abnormal working data of the oversized sample data. This structure of the soft sensor model based on improved Elman NN with variable data selection is shown in Figure

The structure of the soft sensor model based on improved Elman NN with dimension-reduction.

In Figure

In the training process of improved Elman NN, each layer in the feedforward path is considered as one-layer BP network which can update weight parameters by gradient descent. The representation of

The loss function can be the traditional squared error as in equation (

A new set of weights

Then, the prediction model of

After the variable selection and training, the prediction value of the soft sensor model based on improved Elman NN as in equation (

The optimal parameters can be obtained by the minimization of the average BIC values:

The procedure of the soft sensor model based on improved Elman NN with selected variable and dimension-reduction is summarized as follows.

Train a new improved Elman NN by the training dataset and obtain initial weight parameters of the network.

Selection of input variable dataset.

Initialize variable data preprocessing method based on combining ISOMAP with LLE.

For the current variable dataset, calculate approximate geodesic distance to obtain the maximum eigenvalue

Obtain the real symmetric semipositive definite matrix

Calculate

Calculate

Obtain the input variable data without redundancy and noises disturbing.

Evaluate the parameter optimization by equation (

Update the weight parameters by equation (

The rotary kiln is an important part of pellet sintering. Green pellets with a diameter of 9~16 mm are generated in the pellet making system. Then the pellets pass through the kiln tail into the rotary kiln after preheating at the chain grate. In the rotary kiln, the oxidizing roast and consolidation process of pellets is completed, which makes pellets have the physical and chemical properties of the blast furnace burden. To ensure and improve the product quality of pellets, the real-time control of temperature in the rotary kiln calcining process is very important. And the temperature in the rotary kiln calcining process is directly related to production efficiency, energy consumption, and emissions of harmful gas.

By the analysis of the heat balance mechanism and technological characteristics of the rotary kiln calcining process, the temperature in the rotary kiln calcining process is coupled with multiple technological index variables in the grate system and ring cooler system, which makes it very difficult to use the instrument directly to measure the temperature in the rotary kiln calcining process because of poor working conditions or high maintenance costs of hardware sensors. Thus, the soft sensor model based on improved Elman NN with variable data selected and Bayesian optimization is applied to estimate the temperature in the rotary kiln calcining process. For the prediction of the temperature, we use the technological index variables which are correlated with prediction temperature and are easy to measure as the input variables of the soft sensor model in this process, which are listed in Table

Candidate variables of the soft sensor model for temperature prediction in the rotary kiln calcining process.

Variables | Description | Unit |
---|---|---|

The speed of the chain grate | m/min | |

The speed of the rotary kiln | rin/min | |

The speed of the ring refrigerator | m/min | |

The temperature of rotary kiln head | °C | |

The temperature of rotary kiln tail | °C | |

The quantity of coal injection | t | |

I section temperature of the cooler | °C | |

II section temperature of the cooler | °C | |

Material thickness in the chain grate | mm | |

Preheating I section temperature of the smoke hood in chain grate | °C | |

Preheating II section temperature of the smoke hood in chain grate | °C |

According to the technological characteristics of the rotary kiln and technology analysis, the secondary variables are selected based on the combining of ISOMAP with LLE through kernel function, which can simplify the redundant and abnormal data of the selected variables. The secondary variables are chosen as input of the soft sensor model based on improved Elman NN to predict the temperature in the rotary kiln calcining process. The Bayesian optimization criterion is applied to estimate the accuracy of prediction model and adjust the weights in order to amend the error. The structure diagram of temperature prediction in the rotary kiln calcining process based on improved Elman NN with variable data preprocessing is shown in Figure

The diagram of temperature prediction in the rotary kiln calcining process based on improved Elman NN with variable data preprocessing.

For the improved Elman NN training, data samples have been collected and are partitioned into two parts, in which 3000 process datasets of the secondary variables and corresponding temperature in the rotary kiln calcining process are selected for training, and the 1500 process datasets are applied as the testing dataset. At the same time, the data preprocessing method based on the combination of ISOMAP with LLE is used to remove the noise and data redundancy that exist in input data in order to improve prediction performance. Considering that SVM is a state-of-the-art soft sensor model with good generalization ability, the improved Elman NN with variable dataset preprocessing based on ISOMAP and LLE is compared with the soft sensor model based on SVM. The kernel function of SVM is the radial basis kernel function and the number of support vectors in the SVM is specified as 6. In addition, for a fair comparison, the number of hidden nodes and context nodes is the same in the Elman NN and improved Elman NN. And the number of hidden nodes is set to 36.

In the improved Elman NN with data preprocessing experiments, the gradient descent is employed to train the improved Elman NN. The datasets are chosen by the ISOMAP and LLE method. In addition, the parameters are optimized and decided by comparing validation error curves according to Bayesian criterion. Once the weight parameters are fine-tuned, all training data are employed to train the model again. And the learning rate according to the loss’s change is adopted to obtain an excellent performance. To test the prediction performance of the soft sensor model based on different model methods, 100 testing samples are shown in Figures

Comparison of temperature generalization test in rotary kiln between Elman NN and SVM.

Prediction curve of the kiln burning zone temperature

Error curve of the kiln burning zone prediction temperature

Comparison of temperature generalization test in rotary kiln between SVM and improved Elman NN.

Prediction curve of the kiln burning zone temperature

Error curve of the kiln burning zone prediction temperature

Comparison of temperature generalization test in rotary kiln between improved Elman NN and improved Elman NN with ISOMAP and LLE.

Prediction curve of the kiln burning zone temperature

Error curve of the kiln burning zone prediction temperature

Performance comparison results of prediction temperature under different soft sensor models.

Soft sensor model | RMSE | MNE | MPE |
---|---|---|---|

Elman NN | 3.0496 | −4.582 | 5.697 |

SVM | 2.1471 | −4.332 | 3.719 |

Improved Elman NN | 1.3003 | −3.535 | 3.061 |

Improved Elman NN with variable data preprocessing | 0.5450 | −1.275 | 1.941 |

Table

Figures

However, the three methods are limited to handle the noises and data redundancy which exist in input variable data to improve the prediction performance. The soft sensor model based on improved Elman NN with ISOMAP and LLE is able to remove abnormal working condition noise and data redundancy, as shown in Figure

This paper develops a soft sensor model based on improved Elman NN and proposes a data preprocessing method based on ISOMAP and LLE for input variable data selection. The improved Elman NN introduces local feedback and feedforward networks into the Elman NN, which is trained to obtain better generalization and avoid overfitting to a certain extent. The data preprocessing method based on ISOMAP and LLE effectively keeps the neighborhood structure and the global mutual distance of the datasets and better reflects the real character of the original datasets, which is used to remove the abnormal working condition data, noises, and data redundancy in the input variables from improved Elman NN. The soft sensor model based on improved Elman NN with data preprocessing by ISOMAP and LLE is applied to estimate the temperature in the rotary kiln calcining process. The prediction values of the soft sensor model based on improved Elman NN with data preprocessing through ISOMAP and LLE follow the varying trend of the temperature very effectively and have excellent robustness and generalization performance. The great performance illustrates that the soft sensor model based on improved Elman NN with data preprocessing through ISOMAP and LLE provides a powerful and promising method for complex industrial process applications.

The prediction temperature of the rotary kiln calcining process in Sintering and Pelletizing data used to support the findings of this study have not been made available because the data which is used is the proprietary data from a Sintering and Pelletizing company that will share the data only with regulatory agencies but not with researchers. So the jurisdiction of the data is limited.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work was supported in part by the Project by National Natural Science Foundation of China under Grant (61473054).