Discrete Dynamics in Nature and Society

Volume 2016 (2016), Article ID 1548986, 11 pages

http://dx.doi.org/10.1155/2016/1548986

## Management of Uncertainty by Statistical Process Control and a Genetic Tuned Fuzzy System

Center of Life and Food Sciences Weihenstephan, Research Group of Bio-Process Analysis Technology, Technical University of Munich, Weihenstephaner Steig 20, 85354 Freising, Germany

Received 17 January 2016; Accepted 10 May 2016

Academic Editor: Lu Zhen

Copyright © 2016 Stephan Birle et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In food industry, bioprocesses like fermentation often are a crucial part of the manufacturing process and decisive for the final product quality. In general, they are characterized by highly nonlinear dynamics and uncertainties that make it difficult to control these processes by the use of traditional control techniques. In this context, fuzzy logic controllers offer quite a straightforward way to control processes that are affected by nonlinear behavior and uncertain process knowledge. However, in order to maintain process safety and product quality it is necessary to specify the controller performance and to tune the controller parameters. In this work, an approach is presented to establish an intelligent control system for oxidoreductive yeast propagation as a representative process biased by the aforementioned uncertainties. The presented approach is based on statistical process control and fuzzy logic feedback control. As the cognitive uncertainty among different experts about the limits that define the control performance as still acceptable may differ a lot, a data-driven design method is performed. Based upon a historic data pool statistical process corridors are derived for the controller inputs control error and change in control error. This approach follows the hypothesis that if the control performance criteria stay within predefined statistical boundaries, the final process state meets the required quality definition. In order to keep the process on its optimal growth trajectory (model based reference trajectory) a fuzzy logic controller is used that alternates the process temperature. Additionally, in order to stay within the process corridors, a genetic algorithm was applied to tune the input and output fuzzy sets of a preliminarily parameterized fuzzy controller. The presented experimental results show that the genetic tuned fuzzy controller is able to keep the process within its allowed limits. The average absolute error to the reference growth trajectory is 5.2 × 10^{6} cells/mL. The controller proves its robustness to keep the process on the desired growth profile.

#### 1. Introduction

Generally, uncertainty can be considered as a result of some information deficiency of any problem-solving situation [1]. When dealing with bioprocesses under real conditions it is rarely impossible to completely avoid uncertainty. The reasons for uncertainty are quite diverse. On the one hand, there are large variations in raw material quality, especially in the food and beverage sector. On the other hand there is the intrinsic nonlinear behavior of the used microorganisms, which is in most cases still not fully understood. Therefore, existing process models are affected by incomplete or fragmentary knowledge about the underlying mechanisms. With respect to process monitoring and control, uncertainty is almost inseparable from any real-time measurement, resulting from a combination of inevitable measurement errors and resolution limits of applied sensors. And at the cognitive level, uncertainty stems from the vagueness and ambiguity which is inherent in human language and the semantics of assessment [2]. Because of the fact that in most cases the sources of uncertainty cannot be easily solved from a physical point of view, several approaches are proposed in literature that allow handling uncertainties by the use of statistics. A general overview of (multivariate) statistical process control and quality control is given in [3–8] and with special focus on food by [9–11]. With respect to online process observation and quality monitoring the use of online control charts is emphasized [12, 13]. The use of online control charts is a very powerful tool in decision-making. It serves as human-machine interface and thus allows the operator to evaluate the process in real time. By means of simple statistics, they allow calculating and graphically visualizing if the current process is running inside or outside its allowed limits. In order to represent the process, key performance indicators and critical quality attributes have to be defined on a univariate or multivariate basis. There are several charting techniques existing that ease the process of statistical quality control and on a single variable basis they are comprehensively reviewed by [14]. However, the majority of SPC approaches presented in literature consider SPC as a pure monitoring system. Although there has been done quite interesting work making use of fuzzy logic approaches in order to handle uncertainty that is related with the construction [15–20] or the evaluation of control charts with respect to quality attribute changes [21], there is only little investigation that actually takes into account how to integrate the information that is delivered by the SPC system into a feedback control system in order to keep the process within its statistical boarders. This shortcoming is mentioned as well by Woodall, Montgomery, and Stoumbos [22–25].

With respect to automatic process control, fuzzy logic has also become a powerful tool in intelligent control of biological systems due to the capability to handle complex nonlinear processes and uncertainty in data [26–29]. The concept of fuzzy logic was first introduced by Zadeh [30]. It uses the principle of linguistic description by means of IF-THEN algorithms in order to mimic human reasoning and process assessment. Therefore, it is a good platform for controller design that is subjected to uncertain process behavior.

However, the classic fuzzy controller has several drawbacks. In particular, a major drawback is the lack of a learning capability. Classical fuzzy systems are static and their practical implementation and optimization is done by trial and error and based on the experience of an expert knowing the process and how it should be controlled. However, with respect to fast controller implementation and finding the optimal parameter configuration of the fuzzy sets in order to reach the required controller performance, the method of trial and error is quite cumbersome and often results in inefficient and suboptimal configurations of the control parameters. The optimal configuration can be “hidden” in the data. Therefore, in this work a genetic algorithm was used in order to provide additional intelligence and the ability of learning to the fuzzy controller. The genetic algorithm optimizes the control performance on a data-driven approach. The overall control strategy, which is represented by the rulebase, uses the cognitive knowledge of an expert.

In this approach, the process control architecture is realized by an automated feedback control system based on fuzzy logic. The fuzzy system is linked to SPC in order to control and monitor the process of yeast propagation. The developed fuzzy controller adjusts the process temperature in order to keep the process within statistical corridors of the controller input variables, which are the control error and the temporal control error derivative. Within the framework of SPC, the statistical corridors, respectively, upper and lower control limits of the input variables, are derived from historical data of batches that met the required quality specifications. Shewhart control charts (-charts) are used to calculate the ideal trajectory , the upper control (UCL) limit, and the lower control limit (LCL) of the input variables. With respect to the control quality this means that if the control error stays within the statistical borders, the process and the control meet the required and predefined quality and performance criteria with a probability of 99.73%. The adjustment of the fuzzy controller parameters is done by a genetic algorithm. The heuristic search mechanism of the genetic algorithm is able to find the ideal parameter configuration of the fuzzy sets. The advantage therefore lies in the combination of fuzzy and genetic algorithms. The fuzzy system holds the principle expert knowledge of how to best control the process and the genetic algorithm is used to optimize the expert knowledge by providing learning capability and efficient solution finding in a big search space.

#### 2. Materials and Methods

##### 2.1. Control Charts and Data Pool

The standard Shewhart -chart consists of a centerline to monitor the process mean and the upper and lower control limit which are calculated from historic process data. The control limits are usually set at ±3 times the standard deviation from the centerline, which is simply the arithmetic average. This expresses statistically that 99.73% of all batches that run within these limits are meeting the specified quality requirements and can be viewed to be in control.

The process for which the system was developed is the brewer’s yeast propagation process, which is a typical and representative process biased by various sources of uncertainty. In general, yeast propagation is performed as a batch process, whereby the yeast undergoes the different growth phases of a static culture (lag phase, exponential phase, transition or deceleration phase, stationary phase, and degeneration). The individual phase duration and the transition time from one phase to another depend on various factors. For example, the lag phase depends on the physiological state of the inoculum and the specific growth medium [31]. The physiological state in turn depends on storage conditions and the upstream treatment of the yeast used as inoculum [32]. Furthermore, the growth behavior is influenced by the substrate, which is beer wort. Its composition again is dependent on natural variations of the used raw materials. In consequence, the effects of substrate limitations on the metabolic behavior due to unavoidable variations in available carbohydrates, nitrogen, zinc, or vitamins are subjected to uncertainty. Additionally, metabolic regulation effects occurring under brewing related conditions have to be taken into account. In this regard, the most important regulation mechanism affecting the different metabolic pathways is the Crabtree effect [33]. The Crabtree effect, which is also known as overflow metabolism, catabolite repression, aerobic fermentation, or oxidoreductive metabolism, leads to the formation of ethanol at exceedance of a critical glucose concentration in the substrate [34–36]. In summary, the process of oxidoreductive yeast propagation is affected by numerous sources of uncertainty that in consequence influence the observability and controllability of the process. Hence, in order to observe and control this kind of process an intelligent online monitoring and process control system is required.

In this work the data of 11 batches was used that met the following performance and quality requirements:(i)Cell count concentration at end of batch: ≥100 × 10^{6} cells/mL.(ii)Portion of dead cells at end of batch: ≤1%.

For the experimental work, beer wort produced from standard malt extract (Weyermann®, “Bavarian Pilsner”) was used as substrate for the propagation of* Saccharomyces cerevisiae* sp. (strain W34/70). A detailed description of the technical plant configuration, experimental procedure, and analytics is given in [37]. For the performance analysis, calculation of control charts, and the later controller design, a temperature dependent growth model by [38] was implemented. The model is based on known stoichiometric turnover and Michaelis-Menten kinetics of yeast [35, 36, 39]. In addition, it considers growth limitations like the Crabtree effect that occur by feeding substrate sugar concentrations above 100 g/L [33]. The effect of temperature on yeast growth, respectively, the substrate uptake, is modeled by implementing an additional temperature factor that is expressed by a square root term that was originally developed to describe the temperature effect on the growth of specific bacteria [40, 41]. The specific substrate uptake can be represented by the following equations:Applied half saturation constants for limitations or inhibition were = 2.8 mmol/L [36], = 2 mmol/L [42], and = 500 mmol/L [43]. Furthermore, = 0.486 mol/mol/h [36] denotes the maximum specific substrate uptake rate, is the substrate concentration in mmol/L, is the nitrogen concentration in mmol/L expressed as NH_{3} equivalents, and is the ethanol concentration in mmol/L. The lag time is determined by a sigmoid function , where was set to 5.6 h. is the temperature in K and the mathematical regression coefficients were determined to be = 0.03296 and = 11.98 in this work. = 270.7616 K and = 308.1539 K are temperatures where no further growth is observed.

Figure 1 displays the comparison of yeast cell counts (YCC) in mmol/L between the model outputs and the corresponding experimental runs (that were judged as “good” batches from a qualitative point of view) for different temperature profiles. The YCC of the batches was measured online using a turbidity sensor (optek-Danulat, AF 16). The model has a root mean squared error (RMSE) of 7.4 mmol/L and therefore shows good accuracy in predicting the cell concentration. The error between model and real trajectory, as well as its temporal derivative , is then calculated in order to establish the control charts: Due to the varying individual batch length, the batches were uncoupled from time. To achieve this, batch evening was performed by resampling the batches and mapping them to the shortest number of sampling instances. Then, after mean centering and normalization with the standard deviation, for batches with sampling instances, the control charts are calculated as follows: