Automatic detection of spawning in oysters: a fault detection approach 

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Spawning of Oysters

For oysters, the experimental study of spawning dates back to 1938, when American biologist Paul S. Galtsoff published his seminal work on the physiology of reproduction of oysters [68]. Based upon laboratory observation, spawning is a specific/particular type of shell/valve activity of female oysters [23, 85]. In [68], an ostreograph was used to measure the valve activity and that data was later used to study spawning. Under normal environmental conditions shell/valve movements are characterized by long relaxation periods which may vary from a few minutes to hours and are often interrupted by secondary contractions. While during spawning (see Fig. 3.1 or Fig. 3.2, oysters N° 1
and N° 3), it can be seen that a series of rapid contractions and relaxations are occurring following one after another with remarkable regularity and continuing for about 30−40 minutes. Consistency in the amplitude of the relaxation curve, especially during the first half of the reaction and the remarkable rhythmicity of the contractions are the most distinctive features of the sexual reaction of a female. This phenomenon does not occur under any other circumstance. Burst of valve activity can be seen in other  cases as well as under the influence of some external excitation (for example pollution  or chemical injection) but (1) their frequency is never so regular, (2) will last for shorter period of time and (3) will have longer relaxation period. It was also known that spawning propagates from one to another and eventually over a large fraction of the oyster community [68]. Hence, any rhythmic behavior to be considered as spawning should have certain characteristics. For example:
1. regularity in rhythm and consistency in amplitude;
2. happening for 30 − 40 minutes with short relaxation period;
3. simultaneous spawning in the population and so on.
In this chapter, we considered only this type of spawning that is clearly distinguishable. However, spawning can happen with mild characteristics also. For example, instead of 30−40 minutes duration, it can last 10−20 minutes. We will focus in this chapter on detecting any spawning behavior with strong characteristics or clearly distinguishable. Therefore, the spawning behavior can be considered as a deviation from normal behavior. In Fault Detection literature [27, 87], this is known as fault (i.e. deviation from normal behavior). So, the detection of this fault is equivalent to the detection of spawning.

Automatic Detection of Spawning

In the previous Section, details about a spawning behavior were discussed. One point to be noted in this regard is that the detection of spawning is totally manual until now. In Chapter 2, we have tried to establish a relation between water quality and abnormal valve activity [6]. There, we have showed that the deviation of valve activity from normal behavior, if it occurs in the whole animal group can be used as an indicator for change in water quality. Since the spawning behavior is a total deviation from normal behavior, according to [6], it could also be considered as an indicator for change in water quality. However, in reality this is a totally normal behavior having little to do with the occurrence of poor water quality. By automatic spawning detection, we will be able to differentiate spawning behavior with numerous other abnormal motions. Moreover, it will save time and labor of visually analyzing the data to find the period of spawning. So, automatic detection of spawning can be very useful.

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Rhythmicity Information Calculation

During the spawning, the valve movement maintains a very periodic nature. A first step in identifying this pattern of behavior from others is to calculate the minimum and maximum of the signal amplitude for a certain interval (for example 1000 data points). This difference of the minimum and maximum value of the amplitude in this interval has a lower bound or threshold during spawning. If at current sampling instant, the difference of the minimum and maximum value of the amplitude in the interval of the signal exceeds the threshold, we will proceed further, otherwise we can say that spawning is not happening. Since the signal amplitude for different oysters varies widely just by using this criteria we may ignore a lot of potential spawning oysters. In the next step, we will calculate the frequency in this interval. If the frequency crosses a certain threshold, we will proceed to the rest of our algorithm which will use a velocity based detection of spawning. These two criteria will help us to eliminate a lot of data points which will in turn reduce the computational burden. The two criteria can be briefly described as:
• Amplitude criterion: Aint = max(yi−1000,j : yi,j) − min(yi−1000,j : yi,j), Aint ≥ Ath, (3.1).

Table of contents :

Contents
List of Figure
Nomenclature
1 General introduction 
1.1 Background and motivation
1.2 Outline of the thesis
1.3 List of publications
1.3.1 Peer-reviewed international journals
1.3.1.1 Published
1.3.1.2 Submitted
1.3.2 Peer-reviewed international conferences
1.3.3 Local conference
I Environmental monitoring using oysters as bio-sensors 
2 Identification of dynamical model of oysters population for water quality monitoring 
2.1 Introduction
2.2 Measurement System Description
2.3 Model Identification
2.3.1 Models of circadian clocks
2.3.1.1 Hypothesis on clocks
2.3.2 ARMAX model
2.4 Hypothesis selection, verification and analysis
2.4.1 Hypothesis selection
2.4.2 Verification
2.4.3 Application to ecological monitoring
2.5 Conclusion
3 Automatic detection of spawning in oysters: a fault detection approach 
3.1 Introduction
3.2 Spawning of Oysters
3.3 Automatic Detection of Spawning
3.3.1 Rhythmicity Information Calculation
3.3.2 Velocity Estimation
3.3.2.1 Algebraic Differentiator
3.3.2.2 A non-homogeneous HOSM differentiator
3.3.2.3 Homogeneous finite-time differentiator
3.3.3 Filtering of energy signal and spawning detection
3.3.4 Decision rule
3.4 Results and Discussions
3.5 Conclusions
II Synchronization of oscillations 
4 Robustness of Phase Resetting to Cell Division under Entrainment 
4.1 Introduction
4.2 Motivating example
4.3 PRC-based phase model for an oscillator with cell division
4.3.1 Problem statement
4.3.2 Reduced phase model under cell division
4.3.3 Phase synchronization
4.4 Examples
4.4.1 Circadian oscillations in Neurospora
4.4.2 The Repressilator
4.5 Conclusion
5 Robust synchronization for multistable systems 
5.1 Introduction
5.2 Synchronization of multistable systems
5.3 Examples and simulations
5.3.1 Application to nonlinear pendulums without friction
5.3.2 Application to nonlinear pendulums with friction
5.4 Conclusions
6 General Conclusion and future works
6.1 General conclusion
6.2 Future works
References

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