Soft Sensor Calibration Strategy And Method Based On Interpolation For Missing Data Of The Sparsely Sampled Target Variable

In chemical processes,due to technical or economic reasons,it is often difficult to estimate some important quality variables in real-time which are the key indicators of product quality.This problem affects the process control and optimization,and the soft sensor technology is developed for solving it.Decades of soft-sensor-related studies have advanced the development of the soft sensor technology.Although it has been proved that the soft sensor is powerful and effective to estimate those hard-to-measure key variables,like most measuring devices used in the industrial processes regular maintenance is also indispensable for soft sensor.Basically soft sensor can be viewed as an approximation of the objective process model within a particular application domain.Consequently the model mismatch between the soft sensor and the process model is unavoidable.When the model mismatch increases to a significant degree,the soft sensor's performance usually rapidly deteriorates or even comes to a complete malfunction.Therefore,the main work of the maintenance is to assess the severity of the model mismatch and calibrate the soft sensor model online to recover the model's capability of properly describing the property of the objective process.Currently there are mainly three ways of performing sensor calibration: calibration based on the compensation for soft sensor output,calibration based on online update of soft sensor model parameters and calibration implemented by reconstruction of the soft sensor model.However,it should be pointed that all the three basic calibration method require the feedback information of the hard-to-measure target variables.That is to say,the calibration methods cannot perform well if the feedback of target variable is not sufficiently available,i.e.sparse sampling.Apparently the principal contradiction lies in the missing feedback values of the hard-to-measure target variables due to the sparse sampling.In order to solve the data-lacking issue,we proposed some solutions.Basically the main idea of our proposed solutions is to estimate those missing values of the target variables with considerably high reliability and accuracy and use these estimated values to calibrate the soft sensor model.(1)Our preliminary solution is to construct a moving data window by using the sparsely sampled values of the target variable and use Gaussian process regression method to perform interpolation of those missing values over the window.Considering the interpolated missing values are inevitably associated with uncertainty in some way,it is not wise to directly use these values to calibrate the soft senor model,especially when the uncertainty is severe.Together with the uncertainty,the interpolated values form a band of data.Our strategy is to sample from the band to obtain several data sets and apply every one of the data sets to calibrate senor model once.Finally we can obtain a few candidate models of the calibrated soft sensor.First,we assign a prior weight for each of the candidate models by the probability of the corresponding data set occurring in the band.Then we put those candidate models to a validation test under the same condition and assign a posterior weight by their performances.The two weights together determine the ultimate weights of the candidate models.Note that the weight should be further normalized.The soft sensor model is eventually calibrated by a weighted combination of those candidate models.(2)To some extent,the soft sensor calibration method of using Bayesian Gaussian process regression(GPR)based data interpolation can solve the missing-data issue caused by sparse sampling of the target variable.However,it is still risky to apply the method.As the sampling sparsity of the target variable increases,the uncertainty corresponding to those interpolated values over the moving window also increases.Under such a circumstance,the performance of the calibration method is usually not so satisfactory as expected or even comes to a failure.To deal with the problem,we make some significant improvement on the basis of the GPR-based calibration method.We first use Just-in-time(JIT)strategy to perform preliminary estimation for those missing values of the target variable.The next step is to construct a moving data window by using both the preliminarily estimated missing values and those sparsely sampled values.Unlike the GPR-based method,there are more data are involved into the constructed data window.As a result,the uncertainty corresponding to the missing-data area within the data window can be decreased in some way.At the same time,the moving data window is capable of updating its components continuously by adding in some latest data points and dumping some oldest data points.Based on the moving data window,we use AdaBoost learning method to figure out the latent pattern behind the data set of the window by obtaining a proper local describing function.Obviously this function can describe the main behavior of those data points.Because there is still uncertainty mixed in the window,the strategy is to apply this describing function to refine those preliminarily estimated data points within the window.In this step,the uncertainty of the window data set can be further reduced.Finally we pick out some of the latest part of data set to perform sufficient calibration for the soft sensor model.(2)For convenience,we introduce the concept of sampling cycle ratio which is the ratio between the sampling cycle of target variable and that of the process variable.When the cycle ratio is large,the calibration method based on JIT strategy and AdaBoost learning method can achieve better performance than the GPR-based calibration method.However,the performance of the JIT strategy is constrained by the quality of the history database,especially the operation of sampling history data points from the database given a query point.We are not interested in the improvement of the database's quality.Instead,we proposed to improve the performance of the JIT strategy by achieve an estimation of the density information of the data distribution within the database.First,the database is divided into plenty of small data blocks each of which has homogeneous data density.Then we take the centers of those blocks as query points and calculate the proper sampling numbers for those centers.In the next step,those data blocks are put to stand the “pooling process”.Finally the history database is partitioned into several zones and each of the zones corresponds to a data density which can be represented by a particular sampling number.Therefore,given a new query point,we can select a proper sampling number by simply figuring out which zone the query point locates to achieve a more accurate and reasonable sampling of history data points from the database.In this way the performance of the JIT strategy is enhanced by improving the effectiveness and reliability of the utilization of the history database.