صف بندی داده های دسته ایی ناجور با کاربردی برای کنترل کمیت محصول انتهایی دسته Uneven batch data alignment with application to the control of batch end-product quality

In order to assess and validate the above uneven batch data alignment approach, a benchmark simulation for the penicillin fedbatch fermentation process is used. The simulator, called Pensim, is based upon a series of detailed mechanistic models that describe the fermentation process [32]. The following process variables are collected hourly during the fermentation process: aeration rate, agitator power, substrate feed temperature, substrate concentration, dissolved oxygen concentration, culture volume, carbon dioxide concentration, pH, fermenter temperature, generated heat and substrate feed rate. The substrate feed rate is the manipulated process variable while the batch end-product quality is the biomass concentration measured at the end of batch runs. Except for varying substrate feed rate profiles for batch runs, the fed-batch fermentation process is also subject to disturbances to aeration rate, agitator power, substrate feed rate and substrate feed temperature. Furthermore, the solution concentration for the feeding substrate is oscillating around the constant value of 600 g=l as a result of variations in the property of raw materials. All these disturbances or noise on operating conditions and raw materials contribute to varying batch lengths in practice. It is assumed that the target biomass concentration at the end of batch runs is 12 g=l and samples are to be taken out for laboratory assay at 160th and 180th hour to see if the target is met. If the target has been met, the batch run is to be stopped immediately. Otherwise, the batch is to continue running up to the full length of 200 h. So the batches are likely to have the length of 160, 180 and 200 h, respectively. Other criteria for ending a batch run can also be performed to generate batch runs with variable lengths. Taking 40 batches with variable lengths as an example for illustrating the uneven data alignment method, trajectories of biomass concentration for these 40 batches obtained from the simulator are plotted in Fig. 4. It can be seen that these batches are of variable batch lengths and the longest batch lasts 200 h. Note that these biomass concentration trajectories are assumed to be unmeasured but are shown here for illustrative purposes. According to the uneven data alignment method as shown in Fig. 1, these 40 batches are first aligned to their endpoints and a modeling window is selected for identifying the Wm-PCA&Wm-PLS models. The identified Wm-PCA model is further applied to estimate the missing trajectories in shorter batches and therefore all resulting batches are of the same length of 200 h after feeding the missing data. The future substrate feed rate is assumed to be known in advance since it is the process input. Thus it is not estimated by missing data algorithms while all other process variables are to be estimated for shorter batches. Specifically, the missing data algorithm called projection to the plane is applied here. Other missing data algorithms such as trimmed score method can also be applied.