# Gaussian Distribution Model for Detecting Dangerous Operating Conditions in Industrial Fish Farming
## 1 Introduction  
Fish mortality, mainly due to outbreaks, is a factor of great concern for fish farmers and it severely affects production in aquaculture facilities [1, 2, 3]. Over the past decade, tremendous effort has been devoted to developing solutions for this. For instance, outbreaks have constantly been investigated to better identify important pathological and epidemiological pathways of infections, and determine the etiological agents [4, 5, 6]. Several effective control strategies to reduce high levels of mortality can be mentioned, such as disruption of bacterial quorum sensing [7], sampling time and surveillance [8], remote physiological monitoring [9], long-term monitoring [10], enriched rearing [11], and postbiotics applications [12]. Besides, strategies for sustainable aquaculture have also been widely discussed these days to reduce financial losses caused by high mortality rates. Hydrogen peroxide and peracetic acid therapeutics, natural feed supplements, and humic substances are just some of the promising possibilities for this purpose [13]. High levels of nitrite are the cause of severe physiological disturbances that result in mass fish mortality [14, 15]. Nevertheless, the quantity of nitrite required to kill fish changes with each species and may even delay the occurrence of deaths [16, 17]. Besides, if a fish with methemoglobinia is frightened or otherwise forced to become active, it may die of anoxia [18]. This evidence may suggest a possible explanation for the observation of extremely high mortality rates in just a single day [19]. In this way, appropriate nitrite management approaches have also been investigated [20]. Furthermore, one possibility to have better control of fish health and welfare, and consequently reduce the level of mortality, is to apply recirculation aquaculture systems(RAS) that are intensive aquaculture facilities models in which water is partially reused after undergoing treatment [21; 22]. Despite all the benefits that RAS can offer, recent investigations reveal that high mortality rates are still observed in RAS facilities, typically resulting from complex interactions between the fish biomass and water chemistry in the hatchery, and where small variations may result in inadequate conditions for the welfare of fish. These variations can cause stress on the fish, reduce their feed intake, impair their growth rate, and even cause them to die [23; 24]. To optimize fish production, aquaculture facilities have developed to the point of reaching a large industrial scale [25], monitoring several physical parameters such as, alkalinity, bromine, nitrogen dioxide, pH, ammonia, salinity, temperature, among others, at the same time to satisfy a wide range of operating requirements [26]. However, with all this monitoring structure, new problems quickly emerged. Among the most relevant, is the massive amount of data generated that requires an automated acquisition and specialized analysis [27; 28; 29], and also the need for frequent maintenance of the sensor devices [26]. In order to fill this gap and develop a mechanism that would allow an efficient analysis of all these parameters generated by the modern aquaculture enterprises, in previous work, we developed a decision-making tool for monitoring these parameters [19]. With this data processing, all aquaculture parameters can be mapped simultaneously as well as grouped according to their variability. This methodology is useful not only to better regulate the parameters of the hatchery, but also to identify possible causes of mortality. Furthermore, deep learning is nowadays pointed out as a possible solution for smart fish farming. Nevertheless, this data processing tool is still in a weak artificial intelligence stage and demands massive amounts of labeled data for training, which has become a bottleneck that restricts its application in aquaculture enterprises [30]. Additionally, computer vision models with emphasis on fish detection and behavior analysis have also been investigated to address these issues [31].