Integration of Real-Time Sequential Root Cause Analysis and Multivariate Moving Average-Real-Time Sequential Testing Models for Abnormal Fish Movement Detection in Aquaculture Systems

Abstract

In fish farming, monitoring and understanding fish movement patterns are crucial for optimizing farm management and ensuring fish health and welfare. Fish movement behavior within aquaculture systems can provide insights into feeding habits, environmental conditions, and overall well-being. By tracking movements, such as swimming patterns and group dynamics, farm operators can detect anomalies early, indicating potential health issues or environmental stressors. Detecting abnormal fish movement in aquaculture settings is critical for ensuring fish health and farm productivity. This study proposes the application of Real-Time Sequential-Root Cause Analysis (RTS-RCA) and Multivariate Moving Average-Real-Time Sequential Testing (MMA-RTST) models for effective abnormal detection. RTS-RCA identifies potential anomalies by sequentially analyzing real-time data streams, while MMA-RTST enhances detection accuracy through multivariate statistical analysis and sequential testing methodologies. By integrating these models, the system can promptly identify and respond to abnormal fish behaviors, such as erratic swimming patterns or unusual group formations, which may indicate health issues or environmental stressors. RTS-RCA analyzes real-time data streams to identify anomalies with a detection accuracy exceeding 90%. Simultaneously, MMA-RTST employs multivariate statistical analysis to enhance detection sensitivity, achieving a false alarm rate of less than 5%. Integrating these models enables timely identification of abnormal fish behaviors, such as erratic swimming or unusual group formations, crucial for proactive management and maintaining fish health in dynamic aquaculture environments.

Headnote

Keywords: fish farming, fish movement patterns, real-time sequential-root cause analysis (RTS-RCA), multivariate moving average-real-time sequential testing (MMA-RTST), real-time data analysis, multivariate statistical analysis, anomaly detection, proactive management

In fish farming, monitoring and understanding fish movement patterns are crucial for optimizing farm management and ensuring fish health and welfare. Fish movement behavior within aquaculture systems can provide insights into feeding habits, environmental conditions, and overall well-being. By tracking movements, such as swimming patterns and group dynamics, farm operators can detect anomalies early, indicating potential health issues or environmental stressors. Detecting abnormal fish movement in aquaculture settings is critical for ensuring fish health and farm productivity. This study proposes the application of Real-Time Sequential-Root Cause Analysis (RTS-RCA) and Multivariate Moving Average-Real-Time Sequential Testing (MMA-RTST) models for effective abnormal detection. RTS-RCA identifies potential anomalies by sequentially analyzing real-time data streams, while MMA-RTST enhances detection accuracy through multivariate statistical analysis and sequential testing methodologies. By integrating these models, the system can promptly identify and respond to abnormal fish behaviors, such as erratic swimming patterns or unusual group formations, which may indicate health issues or environmental stressors. RTS-RCA analyzes real-time data streams to identify anomalies with a detection accuracy exceeding 90%. Simultaneously, MMA-RTST employs multivariate statistical analysis to enhance detection sensitivity, achieving a false alarm rate of less than 5%. Integrating these models enables timely identification of abnormal fish behaviors, such as erratic swimming or unusual group formations, crucial for proactive management and maintaining fish health in dynamic aquaculture environments.

Povzetek: Članek predstavi kombinacijo modelov RTS-RCA in MMA-RTST za zaznavanje nenavadnega gibanja rib v ribogojnicah s pomočjo večrazsežne statistike in sprotne analize vzrokov.

1 Introduction

In recent years, the detection of abnormal fish movement in fish farms has garnered significant attention due to its crucial role in ensuring the health and productivity of aquaculture operations. Advances in technology have facilitated the development of sophisticated monitoring systems that utilize various sensors and imaging technologies to track fish behavior continuously [1]. Abnormal movement patterns can indicate potential health issues, environmental stressors, or the presence of predators. Machine learning algorithms and computer vision techniques have been increasingly employed to analyze large datasets of fish movements, enabling early detection of anomalies and timely intervention. These innovations not only improve fish welfare but also enhance the efficiency and sustainability of fish farming practices by reducing losses and optimizing resource management [2]. As the aquaculture industry continues to expand, the implementation of such advanced monitoring systems becomes essential in maintaining high standards of production and ensuring the long-term viability of fish farms [3].

Real-time sequential-root cause analysis for abnormal detection of fish movement in fish farms has emerged as a cutting-edge approach to maintaining healthy and productive aquaculture environments [4]. This method involves continuously monitoring fish behavior using advanced sensor networks and imaging technologies to detect unusual movement patterns that may indicate stress, disease, or environmental changes. By applying real-time data analytics and machine learning algorithms, these systems can identify and analyze anomalies as they occur [5]. Sequential-root cause analysis delves deeper by tracing the detected abnormalities back to their origin, providing insights into underlying issues such as water quality fluctuations, feed problems, or the presence of pathogens. This proactive approach allows for immediate corrective actions, minimizing the impact on fish health and farm productivity [6].

Real-time sequential-root cause analysis with automated alert systems further streamlines the response process. When an abnormal movement pattern is detected, the system can promptly notify farm managers through various communication channels, such as mobile apps or control center dashboards [7]. This immediate notification allows for swiftintervention, whether it involves adjusting environmental parameters, administering treatments, or modifying feeding strategies [8]. Additionally, historical data collected through continuous monitoring can be used to refine predictive models, making future detections even more accurate and efficient. The combination of advanced technologies and real-time analysis not only improves fish welfare and farm productivity but also reduces operational costs by preventing large-scale losses [9]. As the aquaculture industry faces increasing demands for sustainable and efficient practices, real-time sequential-root cause analysis stands out as a pivotal innovation, driving the future of fish farming towards greater resilience and profitability [10-15].

The integration of Real-Time Sequential-Root Cause Analysis (RTS-RCA) with Multi-Modal Adaptive Real-Time Surveillance and Tracking (MMA-RTST) models represents a significant advancement in the abnormal detection of fish movement in fish farms. These integrated systems leverage the strengths of both methodologies to provide a comprehensive and robust monitoring solution. RTS-RCA focuses on continuously monitoring and analyzing fish behavior to identify and trace anomalies back to their root causes, while MMARTST incorporates multiple data sources and adaptive algorithms to enhance the accuracy and reliability of surveillance and tracking processes [16-20]. By combining these models, fish farms can achieve unprecedented levels of precision in detecting abnormal fish movements. The MMA-RTST model utilizes various sensors and imaging technologies to gather diverse data types, such as visual, acoustic, and environmental parameters. This multi-modal approach ensures a holistic view of the fish farm environment, allowing for the detection of subtle and complex behavioral changes that single-sensor systems might miss. The adaptive nature of MMA-RTST enables the system to adjust to varying conditions and maintain high performance even in dynamic and challenging environments [21]. When integrated with RTS-RCA, the collected data undergoes real-time sequential analysis to pinpoint the root causes of detected anomalies. This integration allows for rapid and accurate identification of issues such as disease outbreaks, water quality deterioration, or suboptimal feeding practices. Consequently, farm managers can receive timely alerts and actionable insights, facilitating swiftand effective interventions to mitigate potential problems. The synergy between RTS-RCA and MMARTST models not only enhances the overall efficiency and sustainability of fish farming operations but also improves fish welfare by ensuring a healthier and more stable environment. As the aquaculture industry continues to evolve, the adoption of such integrated monitoring systems will be crucial in meeting the growing demands for food security and environmental stewardship [22-25].

This paper makes significant contributions to the field of aquaculture by advancing the methodologies for detecting and analyzing anomalies in fish movement. Firstly, it introduces and integrates the Real-Time Sequential-Root Cause Analysis (RTS-RCA) and Multivariate Moving Average-Real-Time Sequential Testing (MMA-RTST) models, providing a novel framework for identifying and diagnosing deviations in fish behavior and environmental conditions. The paper's comprehensive simulation analyses validate the effectiveness of these models, demonstrating their capacity to detect a range of anomalies with high accuracy while minimizing false positives and negatives. Additionally, the study offers detailed insights into the application of these models across various scenarios, such as water quality drops and temperature spikes, thereby contributing valuable knowledge to the management of fish farms. By addressing both real-time detection and root cause analysis, the paper lays the groundwork for more effective monitoring systems, enhancing fish welfare and operational efficiency in aquaculture. The contributions of this work not only advance theoretical understanding but also have practical implications for improving aquaculture practices and ensuring sustainable fish farming [26].

2 Related works

In recent years, the field of fish farming has witnessed substantial advancements in monitoring and analyzing fish behavior to enhance farm productivity and fish welfare. Abnormal detection of fish movement has become a critical focus, driven by the need to identify early signs of health issues, environmental stressors, and other potential threats. Various methods and technologies have been explored to address this challenge, including real-time sequential-root cause analysis (RTS-RCA) and multi-modal adaptive real-time surveillance and tracking (MMA-RTST). This section reviews the related works in this domain, highlighting the key developments and innovations in sensor technologies, machine learning algorithms, and integrated monitoring systems. The synthesis of these approaches provides a comprehensive understanding of how real-time data analytics and advanced surveillance models are being utilized to detect and respond to abnormal fish movements, thereby promoting sustainable and efficient fish farming practices.

Ranjan et al. (2023) introduced MortCam, an AI-aided system designed to detect and alert fish mortality in recirculating aquaculture setups, demonstrating its potential in maintaining fish health and optimizing farm operations. Similarly, Jang et al. (2022) utilized deep learning-based image analysis to identify abnormal behaviors in rock bream, showcasing the efficacy of AI in behavioral detection. Chen et al. (2022) developed an underwater abnormal classification system employing deep learning to enhance monitoring precision in Taiwanese fish farms. Li et al. (2022) reviewed intelligent recognition methods for detecting fish stress behaviors, highlighting the rapid progress in AI applications within the industry. Xu et al. (2024) explored the use of machine vision to assess fish responses to ammonia nitrogen stress, further expanding the utility of visual data in aquaculture monitoring. Liu et al. (2023) discussed the advancements in computer vision technology for abnormal fish detection, emphasizing the growing reliance on visual analytics in fish welfare management. Cui et al. (2024) provided a comprehensive review of digital aquaculture technologies, including tracking, counting, and behavioral analysis, underscoring the transformative impact of digital tools on fish farming practices. Huang et al. (2022) employed graph convolutional networks to recognize fish behavior, illustrating the integration of advanced AI models in aquaculture.

Pai et al. (2022) and Mei et al. (2022) highlighted the use of computer vision for behavioral studies and fish counting, and target tracking applications in aquaculture, respectively, reflecting the increasing sophistication of monitoring systems. Calduch-Giner et al. (2022) examined the use of bio-loggers for tracking fish welfare, adding another layer of real-time monitoring capabilities. Zhao (2023) and Patro et al. (2023) further contributed to the field with deep learning and IoT-based approaches for abnormal behavior detection and ornamental fish behavior analysis. Li et al. (2023) reviewed deep learning applications for visual recognition and detection of aquatic animals, indicating a broadening scope of AI in aquaculture. Wu et al. (2022) focused on quantifying locomotor posture and swimming intensity under starvation stress, highlighting specific applications of behavioral analysis. Li and Du (2022) provided an overview of deep learning algorithms for machine vision in aquaculture, reinforcing the central role of AI in modern fish farming practices. Finally, Hu et al. (2022), Zheng et al. (2022), Liu et al. (2023), and Liu et al. (2024) presented various AI and machine learning models for abnormal behavior recognition and multi-object tracking, collectively advancing the frontier of aquaculture technology.

Recent advancements in aquaculture monitoring and management have significantly benefited from the integration of artificial intelligence (AI) and machine learning (ML) technologies. Studies such as Ranjan et al. (2023) and Jang et al. (2022) have demonstrated the effectiveness of AI in detecting fish mortality and abnormal behaviors using image analysis. Chen et al. (2022) and Xu et al. (2024) showcased the use of deep learning and machine vision for precise monitoring in fish farms. Comprehensive reviews by Liu et al. (2023) and Cui et al. (2024) emphasized the transformative impact of computer vision and digital aquaculture technologies on tracking, counting, and behavioral analysis. Advanced models like graph convolutional networks (Huang et al., 2022) and IoT-based approaches (Patro et al., 2023) have further enhanced the detection of abnormal fish behaviors.

3 Fish movement estimation in fishtank

Fish movement estimation in fish tanks involves tracking and analyzing the trajectories of individual fish to understand their behavior and health. This process typically combines image processing techniques and mathematical models to accurately estimate the position and movement of fish over time. High-resolution cameras or other imaging sensors are used to capture continuous video footage of the fish tank. Each frame l(t) represents a snapshot of the tank at time ôeuro . To isolate the fish from the background, background subtraction techniques are applied. This involves comparing each frame l(t) with a background model B computed using equation (1)

... (1)

In equation (1) F(t) is the foreground image highlighting the fish. Object detection algorithms, such as those based on convolutional neural networks (CNNs), are used to identify the bounding boxes of fish within each frame. For each detected fish, we denote its position as (xt, yt) at time t . The positions of fish across consecutive frames are linked to form trajectories. One common method for this is the Kalman filter, which estimates the state of a moving object over time in the presence of noise. The state vector Xt for a fish might include its position and velocity stated in equation (2)

...(2)

The Kalman filter equations include are stated in equation (3) and equation (4)

...(3)

...(4)

In equation (4) A is the state transition matrix, B is the control input matrix, ut - 1 is the control vector, wt - 1 is the process noise, and P is the error covariance matrix stated in equation (5) - (7)

...(5)

...(6)

...(7)

In equation (5) - (7) Kt is the Kalman gain, H is the observation matrix, R is the measurement noise covariance, zt is the observation vector, and is the identity matrix. The movement of each fish can be estimated by calculating the displacement and velocity between frames. For a fish with positions (xt, yt) and (xt + 1,yt + 1) in consecutive frames defined in equation (8) - (10)

...(8)

...(9)

... (10)

In equation (8) - (10) Δt is the time interval between frames. By analyzing the trajectories and velocities of fish, patterns of normal and abnormal behaviors can be identified. For instance, erratic movements may indicate stress or disease. The estimation of fish movement in fish tanks is a multi-step process that involves image acquisition, background subtraction, fish detection, tracking with Kalman filters, and motion estimation. These steps, supported by mathematical models and equations, enable precise monitoring of fish behavior, contributing to improved fish welfare and aquaculture management.

A. Real-Time Sequential-Root cause analysis

Real-Time Sequential-Root Cause Analysis (RTS-RCA) for fish movement detection in fish farms is an advanced approach that leverages real-time data acquisition, processing, and analysis to identify and trace the origins of abnormal fish behaviors. High-resolution cameras and sensors capture continuous video footage and environmental data from the fish tank. Let I(t) denote the image frame captured at time ôeuro , and E(t) represent the environmental data. Once an anomaly is detected, the RTS-RCA framework traces back through the sequence of states and environmental conditions to identify potential root causes. This involves analyzing the sequence of deviations {dt,dt-1,...,dt-n} and corresponding environmental data {E(t),E(t-1),...,E(t-n)}. Real-Time Sequential-Root Cause Analysis (RTS-RCA) is an advanced framework designed to detect, analyze, and address anomalies in fish movement within aquaculture systems in real time. This methodology integrates real-time data processing with sequential analysis to trace the origins of abnormal behaviors. RTS-RCA effectively integrates real-time data acquisition, Kalman filtering for tracking, anomaly detection, and root cause analysis to provide a comprehensive solution for monitoring fish behavior in aquaculture systems. The combination of mathematical models and real-time processing ensures accurate detection of abnormalities and timely intervention, ultimately enhancing fish welfare and operational efficiency in fish farms shown in Figure 1.

Real-Time Sequential-Root Cause Analysis (RTS-RCA) is a sophisticated methodology used to monitor and analyze fish behavior in aquaculture systems by integrating real-time data processing with sequential analysis to identify and address abnormalities. This approach begins with the continuous collection of data from sensors and cameras, which provides both visual and environmental information about the fish tank. The real-time data is then processed to isolate fish from the background using background subtraction techniques, enabling precise tracking of their movements. Fish movement is tracked using the Kalman filter, a recursive algorithm that estimates the position and velocity of each fish over time. The Kalman filter operates through prediction and update steps, using state transition matrices to forecast future positions and correction steps to refine these predictions based on observed data. Any significant deviations from expected movement patterns are flagged as anomalies. When an anomaly is detected, RTS-RCA traces back through the sequence of detected deviations and corresponding environmental conditions to determine potential root causes. This sequential analysis involves examining historical data to identify patterns or changes that may have led to the abnormal behavior. By correlating these findings with real-time observations, RTS-RCA enables the identification of underlying issues, such as changes in water quality or environmental stressors. Finally, RTS-RCA generates real-time alerts to notify farm managers of detected anomalies and their potential causes, facilitating prompt corrective actions. This integrated approach ensures that fish health and welfare are continuously monitored, enabling timely interventions to maintain optimal conditions in the fish farm. The Real-Time Sequential- Root Cause Analysis process in Fish farm is shown in Figure 2.

4 Multivariate moving average-realtime sequential testing (MMARTST)

Multivariate Moving Average-Real-Time Sequential Testing (MMA-RTST) is an advanced statistical methodology used for detecting anomalies and testing hypotheses in real-time data streams, particularly in complex systems like fish farms. The Multivariate Moving Average (MMA) model is used to capture and model the relationships between multiple time series variables. In the context of fish farms, these variables might include fish movement metrics, environmental factors, and operational parameters. For a time series ôeuroœ»ôeuro § with p variables, the MMA model of order ôeuro is expressed as in equation (11)

...(11)

In equation (11) Yt is the vector of observed variables at time t; μ is a vector of constants (mean values); Ci are matrices of coefficients for the lagged error terms and et is a vector of white noise errors at time t. The model helps in understanding the underlying structure of the time series data by estimating the relationship between current observations and past error terms. Real-Time Sequential Testing (RTST) is used to perform hypothesis testing as new data becomes available, allowing for continuous monitoring and immediate detection of anomalies. The testing involves comparing the observed data against the model's expected values. In RTST, we test the null hypothesis H0 that there are no anomalies or deviations from the expected behavior, against the alternative hypothesis H1 that deviations exist. Let Yt be the observed data vector at time t, and Yt be the forecasted values from the MMA model. The residuals et are computed as in equation (12)

...(12)

The test statistic for detecting anomalies is often based on the Mahalanobis distance of the residuals defined in equation (13)

...(13)

In equation (13) ôeuroœµ is the covariance matrix of the residuals. In a fish farm scenario, MMA-RTST can be used to continuously monitor various metrics such as fish movement, water quality, and other environmental factors. By applying the MMA model, the system captures the multivariate relationships and dynamics between these variables. RTST then allows for the realtime detection of deviations from normal behavior, facilitating prompt interventions to address potential issues. Multivariate Moving Average-Real-Time Sequential Testing (MMA-RTST) provides a powerful framework for real-time monitoring and anomaly detection in complex systems. By combining multivariate modeling with sequential hypothesis testing, MMARTST ensures that deviations from expected behavior are detected promptly, enabling timely corrective actions and maintaining system stability. Multivariate Moving Average-Real-Time Sequential Testing (MMA-RTST) is a sophisticated methodology designed to detect and analyze anomalies in complex time series data, such as those found in fish farms. This approach combines the power of multivariate moving average models with realtime hypothesis testing to provide a robust framework for monitoring and decision-making. The process begins with the Multivariate Moving Average (MMA) model, which captures the relationships between multiple time series variables, such as fish movement metrics and environmental factors. The model forecasts expected values based on historical data and the observed patterns of these variables. As new data arrives, the model is continuously updated to reflect the most recent observations.

Real-Time Sequential Testing (RTST) is then applied to these updated forecasts to detect anomalies. Residuals, calculated as the difference between observed values and forecasted values, are analyzed using the Mahalanobis distance, which measures how far the residuals deviate from the expected range. This distance is compared against a critical value from the chi-squared distribution to determine if the deviation is significant. If an anomaly is detected, it is logged, and real-time alerts are generated to facilitate immediate corrective actions. The model is periodically reviewed and adapted to ensure accuracy as conditions change. By integrating real-time data analysis with statistical testing, MMARTST enables effective monitoring and timely intervention, thereby enhancing the management and operational efficiency of aquaculture systems.

5 Simulation analysis

The datasets used for fish movement estimation vary in size, diversity, and acquisition methods. They are collected from real-world fish tanks, aquaculture systems, or simulated environments. Real-world datasets typically include high-resolution video frames, fish position coordinates, and environmental factors such as water temperature, pH, and oxygen levels. These datasets can contain thousands to millions of frames, depending on the duration of recording and frame rate. Some datasets focus on a single species (e.g., zebrafish, tilapia), while others include multiple species to study behavioral differences. Simulated datasets use computational models such as agent-based models and neural networks to generate synthetic fish movement patterns under controlled conditions. These simulations replicate realworld scenarios, including environmental variations, predator interactions, and sudden water quality changes. The table 2 below summarizes key aspects of real-world and simulated datasets.

The dataset for fish movement, as presented in Table 2, consists of both real-world and simulated data sources. Real-world datasets are captured using high-resolution cameras (1080p-4K), leading to dataset sizes ranging from 10,000 to 5,000,000 frames, whereas simulated datasets, generated using AI-based agent models, contain 50,000 to 10,000,000 frames. The number of fish in realworld datasets varies between 10 and 10,000 per dataset, while simulations allow for a range of 1 to 5,000 virtual fish, with greater flexibility in species diversity (1-100 species vs. 1-50 in real-world data). The frame rates differ slightly, with real-world recordings achieving up to 240 FPS, whereas simulations typically range between 30 and 120 FPS. Additionally, real-world datasets record environmental parameters such as temperature (15- 30°C), pH (6.5-8.5), and oxygen levels (4-10 mg/L), while simulated environments offer full customization.

The Table 3 provides a statistical comparison between real-world and simulated datasets. The frame rate (p = 0.03) and fish count per dataset (p = 0.04) show significant differences, indicating that simulations typically produce higher frame rates and contain more fish per dataset. Tracking accuracy between real-world (92 ± 5%) and simulated datasets (95 ± 3%) shows no significant difference (p = 0.08), suggesting that both methods provide reliable tracking. However, environmental variability, measured in temperature fluctuations (p = 0.01), is significantly higher in realworld conditions (2.5 ± 0.8°C) than in simulations (1.0 ± 0.3°C), where conditions are more controlled. The trajectory deviation (p = 0.02) also shows significant variation, with real-world fish movements being less predictable (0.8 ± 0.3 cm) compared to simulated ones (0.5 ± 0.2 cm). However, velocity (p = 0.12) and behavioral anomalies (p = 0.07) do not show statistically significant differences, indicating that the movement and behavioral patterns of fish are relatively consistent across both data sources.

Simulation analysis for Multivariate Moving Average-Real-Time Sequential Testing (MMA-RTST) is a critical tool for evaluating and refining the anomaly detection capabilities in fish tanks. This approach leverages computational models to replicate the behavior of fish and their environment, allowing researchers to test and validate the effectiveness of the MMA-RTST methodology under various scenarios. Simulation analysis for MMA-RTST in fish tanks provides a valuable tool for testing and optimizing anomaly detection systems. By simulating various scenarios and introducing synthetic anomalies, researchers can evaluate the effectiveness of the MMA-RTST approach, refine its parameters, and ensure its robustness in detecting deviations from normal behavior.

In Table 4 and Figure 3(a) - (c) the Moving Average Estimation for the Fish Tank summarizes the performance of the Multivariate Moving Average (MMA) model in forecasting fish tank conditions across various scenarios. In Normal Conditions, the forecasted value of 15.2 closely matches the observed value of 15.3, resulting in a minimal residual of 0.1. Both the mean residual and standard deviation are low (0.0 and 0.1, respectively), and the Mahalanobis distance is 0.1, indicating no significant deviation from the norm. Thus, no anomaly is flagged. For the Water Quality Drop scenario, the forecasted value remains at 15.2, but the observed value drops to 13.8, creating a larger residual of -1.4. This scenario exhibits a mean residual of -0.3 and a higher standard deviation of 1.2. The Mahalanobis distance of 1.6 is notable, leading to the detection of an anomaly. In the case of a Temperature Spike, although the forecasted value is unchanged at 15.2, the observed value rises to 17.5, resulting in a significant residual of 2.3. The mean residual here is 0.5, with a standard deviation of 1.5, and the Mahalanobis distance reaches 2.0, indicating a substantial deviation and flagging it as an anomaly. Feeding Disruption shows a minor discrepancy with a forecasted value of 15.2 and an observed value of 15.0, producing a small residual of - 0.2. The mean residual is -0.1 with a standard deviation of 0.2, and the Mahalanobis distance is 0.2. These values are within normal limits, so no anomaly is detected.

In the Fish Behavior Change scenario, the forecasted value of 15.2 is closely matched by the observed value of 15.4, yielding a minimal residual of 0.2. With a mean residual of 0.1, a standard deviation of 0.2, and a Mahalanobis distance of 0.2, the data does not indicate an abnormal movement. The Equipment Malfunction scenario presents a forecasted value of 15.2, but the observed value drops significantly to 12.5, resulting in a large residual of -2.7. The mean residual is -0.5, with a high standard deviation of 2.0. The Mahalanobis distance is 2.8, suggesting a significant deviation and identifying it as an abnormal movement. Finally, in the Algae Bloom scenario, the forecasted value of 15.2 is nearly matched by the observed value of 15.1, creating a minimal residual of -0.1. The mean residual is 0.0, with a standard deviation of 0.3, and the Mahalanobis distance is 0.3, which is not sufficient to flag an abnormal movement.

The Table 5 MMA-RTST for Fish Movement Estimation provides a comprehensive overview of the metrics used in the Multivariate Moving Average-Real- Time Sequential Testing (MMA-RTST) model to evaluate fish movement in a tank. Each metric represents a key aspect of fish behavior and movement, measured through various methods.

* Movement Speed is measured in centimeters per second (cm/s) and falls within a typical range of 5 to 20 cm/s. This metric is assessed using speed sensors and video analysis, providing insights into how quickly fish are swimming.

* Swimming Patterns are categorized into schooling, random, or directional behaviors. This classification is determined through video analysis and behavioral observation, helping to understand the general movement organization of the fish.

* Activity Levels are recorded in counts per hour, with a typical range of 50 to 200 counts/hour. This metric is measured using motion sensors and video analysis, indicating the frequency of movement or activity in the tank.

* Spatial Distribution measures the percentage of the tank's area covered by fish, typically ranging from 60% to 80%. This is tracked using tracking systems and video analysis to assess how the fish are distributed spatially within the tank.

* Group Density is expressed in terms of the number of fish per square meter (fish/m ), with a typical range of 1 to 3 fish/m . This metric is determined through spatial tracking and manual counts, providing information on the density of fish in different areas of the tank.

* Behavioral Patterns categorize fish behaviors such as feeding, resting, or aggressive actions. These patterns are identified using video analysis and behavioral observation, revealing the types of activities the fish are engaged in.

* Path Trajectory involves the tracking of the paths taken by fish, which can exhibit various patterns. This metric is assessed using tracking systems and video analysis to analyze how fish move through the tank.

* Anomalous Movements refer to deviations from normal movement patterns, such as erratic or high-speed movements. This is detected using anomaly detection algorithms and video analysis to identify unusual behaviors that may indicate problems.

* Interaction Frequency measures how often fish interact with each other, recorded in counts per hour within a range of 30 to 100 counts/hour. Social interaction sensors and video analysis are used to track these interactions.

* Reaction to Stimuli captures the time it takes for fish to react to external stimuli, with a typical reaction time ranging from 1 to 5 seconds. Experimental setups and video analysis are employed to measure this response time.

The Table 6 and Figure 4 -10 Anomaly Detection of Fish Movement in Fish Tank presents the results of applying anomaly detection techniques to various scenarios affecting fish movement in a tank. Each row in the table corresponds to a different scenario, detailing the performance metrics of the anomaly detection system.

* Normal Conditions show no anomalies, with the detection system achieving a perfect model accuracy of 100%. No critical values or Mahalanobis distances are applicable, as no anomalies are present.

* For the Water Quality Drop scenario, characterized by a sudden drop in oxygen, the detection sensitivity is high at 95%. The system shows 2 false positives and 3 false negatives, with an average detection time of 12 seconds. The model's accuracy is 93%, with a critical value of 15.00 and a Mahalanobis distance of 16.24, indicating a robust response to this type of anomaly.

* In the Temperature Spike scenario, involving a sudden rise in temperature, the detection sensitivity is 90%. There are 3 false positives and 2 false negatives, with a detection time of 10 seconds. The model accuracy is 91%, with a critical value of 16.00 and a Mahalanobis distance of 17.85, reflecting a slightly more challenging detection process but still effective.

* The Feeding Disruption scenario, marked by inconsistent feeding, has a detection sensitivity of 85%. The system experiences 4 false positives and 4 false negatives, with a longer detection time of 14 seconds. The model's accuracy is 87%, with a critical value of 14.50 and a Mahalanobis distance of 15.98, indicating some difficulty in detecting this anomaly type.

* For Fish Behavior Change, where aggressive behavior is observed, the detection sensitivity is 92%. There is only 1 false positive and 2 false negatives, with a detection time of 11 seconds. The model achieves an accuracy of 94%, with a critical value of 15.50 and a Mahalanobis distance of 16.70, demonstrating effective detection of behavioral changes.

* The Equipment Malfunction scenario, involving sensor failure, shows the lowest detection sensitivity at 80%. The system reports 5 false positives and 6 false negatives, with the highest detection time of 15 seconds. The model accuracy is 82%, with a critical value of 17.00 and a Mahalanobis distance of 19.32, indicating challenges in detecting equipment-related anomalies.

* Lastly, the Algae Bloom scenario, characterized by excessive algae growth, has a detection sensitivity of 88%. It results in 3 false positives and 3 false negatives, with a detection time of 13 seconds. The model accuracy stands at 89%, with a critical value of 16.50 and a Mahalanobis distance of 17.40, demonstrating a competent but not perfect detection capability for this scenario.

6 Discussions

The simulation analysis of the Multivariate Moving Average-Real-Time Sequential Testing (MMA-RTST) for abnormal movement detection in fish tanks presents a comprehensive method for evaluating and optimizing the system's ability to detect deviations from normal behavior. By leveraging computational models to replicate fish and environmental conditions, this approach enables the testing and validation of the MMARTST methodology in various real-world scenarios. In Table 1, the Moving Average Estimation for the Fish Tank scenario data highlights how the MMA model performs across a range of conditions. The Normal Conditions show minimal deviation between the forecasted and observed values, yielding low residuals and Mahalanobis distances, with no anomalies detected. On the other hand, more extreme scenarios, such as the Water Quality Drop and Temperature Spike, result in larger residuals and higher Mahalanobis distances, successfully flagging anomalies. These deviations underscore the system's capacity to identify disruptions like sudden environmental changes or system malfunctions, as seen in the Equipment Malfunction scenario, where a large residual and high Mahalanobis distance point to a significant issue.

In Figure 3 further demonstrates the computation of residuals, average distances, and abnormal movement estimates, providing visual evidence of how the MMARTST methodology detects changes in fish behavior and tank conditions. The effectiveness of abnormal movement detection improves as deviations from the forecasted values increase, as reflected in higher Mahalanobis distances and flagged anomalies in more disruptive scenarios. In table 2, the MMA-RTST model employs several metrics to track fish movement and behavior, such as movement speed, swimming patterns, activity levels, and spatial distribution. These metrics allow for a detailed understanding of fish behavior under normal and anomalous conditions, providing essential data for abnormal movement detection algorithms. The sensitivity of these metrics to changes in behavior, such as erratic movements or altered swimming patterns, is crucial for timely intervention and maintaining a healthy tank environment. Table 3 expands on the abnormal movement detection process, presenting the sensitivity, false positives, false negatives, and detection time for various abnormal movement scenarios. The model demonstrates high sensitivity in detecting anomalies such as Water Quality Drops, Temperature Spikes, and Fish Behavior Changes, with model accuracies ranging from 82% to 94%. However, challenges arise in scenarios like Equipment Malfunction, where detection sensitivity drops to 80%, resulting in a higher number of false positives and false negatives. This highlights the potential for further refinement in the detection algorithm, particularly for equipment-related anomalies. The MMA-RTST methodology proves to be a valuable tool for simulating, testing, and optimizing abnormal movement detection systems in fish tanks. The system shows strong performance in detecting significant environmental and behavioral anomalies, though some areas, like equipment malfunctions, require further enhancement. The integration of real-time sequential testing with multivariate moving averages allows for precise and timely identification of disruptions, ensuring the health and safety of aquatic life in the tank.

7 Conclusions

This paper presents a comprehensive examination of advanced techniques for detecting anomalies in fish movement within aquaculture environments. By integrating the Real-Time Sequential-Root Cause Analysis (RTS-RCA) and the Multivariate Moving Average-Real-Time Sequential Testing (MMA-RTST) models, we have demonstrated an enhanced approach to monitoring and identifying deviations in fish behavior and environmental conditions. The RTS-RCA model effectively identifies root causes of abnormal movements, while the MMA-RTST model provides robust real-time detection capabilities, supported by detailed simulation analyses. The results highlight the efficacy of these models in various scenarios, including water quality drops, temperature spikes, and equipment malfunctions, showcasing their ability to improve accuracy and reduce false positives and negatives. Despite the challenges in certain scenarios, such as equipment malfunctions, the models consistently deliver high accuracy and valuable insights. This study underscores the importance of combining sophisticated analytical methods with real-time monitoring to ensure the optimal management and welfare of fish in aquaculture settings. Future research could focus on further refining these models, exploring additional anomaly types, and integrating more advanced detection algorithms to enhance overall system performance.

Sidebar

Received: November 25, 2024

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