Symmetry-Enhanced LSTM-Based Recurrent Neural Network for Oscillation Minimization of Overhead Crane Systems during Material Transportation

Abstract

This paper introduces a novel methodology for mitigating undesired oscillations in overhead crane systems used in material handling operations in the industry by leveraging Long Short-Term Memory (LSTM)-based Recurrent Neural Networks (RNNs). Oscillations during material transportation, particularly at the end location, pose safety risks and prolong carrying times. The methodology involves collecting sensor data from an overhead crane system, preprocessing the data, training an LSTM-based RNN model that incorporates symmetrical features, and integrating the model into a control algorithm. The control algorithm utilizes swing angle predictions from the symmetry-enhanced LSTM-based RNN model to dynamically adjust crane motion in real time, minimizing oscillations. Symmetry in this framework refers to the balanced and consistent handling of oscillatory data, ensuring that the model can generalize better across different scenarios and load conditions. The LSTM-based RNN model accurately predicts swing angles, enabling proactive control actions to be taken. Experimental validation demonstrates the effectiveness of the proposed approach, achieving an accuracy of approximately 98.6% in swing angle prediction. This innovative approach holds promise for transforming material transportation processes in industrial settings, enhancing operational safety, and optimizing efficiency.

1. Introduction

Overhead crane systems are essential for material handling in various industries, providing efficient and precise transportation of heavy loads in confined spaces. However, these systems frequently face a significant issue: unwanted oscillations during material transport [1,2]. These oscillations, especially noticeable during the final stages of load delivery, reduce operational efficiency and pose safety risks to personnel and equipment. Reducing oscillations in overhead crane systems is crucial for improving safety, minimizing load sway, and optimizing material handling. Among the factors affecting crane oscillations, the swing angle is a key parameter that greatly impacts system stability and performance [3]. The specific problem this study is seeking to address is the fluctuation and swing of loads during transportation, which not only poses a significant safety risk [4] but also increases transit time, thereby reducing overall operational efficiency. Fluctuations and load swings during crane operations [5,6] are a critical issue in industrial settings. These movements can lead to accidents, damage to goods, and increased wear and tear on the crane system. Traditional control methods often fail to adequately address these issues due to their inability to predict and adapt to real-time changes in the load’s behavior. Thus, there is a pressing need for an advanced control algorithm capable of providing accurate predictions and adjustments to improve safety [7] and efficiency. Various studies have explored different approaches to mitigate load swings in overhead crane systems. Some have focused on traditional control methods [8,9], such as Proportional-Integral-Derivative (PID) controllers, which are straightforward but often lack the adaptability needed for dynamic and complex industrial environments. Other research has utilized more sophisticated techniques like fuzzy logic [10] controllers and model predictive control (MPC). While these methods offer improved performance over traditional controllers, they still face limitations in handling highly dynamic and uncertain conditions effectively. Recent advancements in AI and machine learning [11,12] have introduced new possibilities for crane control systems. Studies utilizing machine learning algorithms, particularly neural networks [13,14], have shown promise in predicting and controlling load swings with higher accuracy. However, many of these approaches are either computationally intensive or require extensive amounts of high-quality training data, which can be challenging to obtain and process in industrial settings. Building on the insights from previous research, this study utilizes the LSTM-based RNN [15,16] model due to its proficiency in handling time-series data and making predictions based on sequential patterns. By integrating this advanced AI technique into the control algorithm, the study aims to provide a more responsive and adaptive solution to the problem of load swings in overhead crane systems. The swing angle, defined as the deviation of the load from its intended trajectory (as shown in Figure 1), is influenced by dynamic interactions between the crane structure, the transported load, and external forces such as wind and inertia.

The integration of symmetry in this study addresses the oscillatory challenges faced by overhead crane systems. Symmetry principles apply to the crane’s structural design, control algorithms, and operational protocols, which significantly enhance balance and stability. A symmetrical distribution of mass and uniformity in crane components can reduce uneven loading and stress points, thereby minimizing oscillation tendencies. In terms of control strategies, symmetrical patterns in motion planning and feedback mechanisms lead to more predictable and stable responses to dynamic forces. Understanding the underlying theory governing swing angle dynamics [17,18] is essential for devising effective control strategies to mitigate oscillations in overhead crane systems.

The swing angle $\left(\theta \right)$ is primarily influenced by the interplay of gravitational forces, inertial forces, and damping effects within the crane system. The governing differential equation for the swing angle can be expressed as follows:

$$mL{\displaystyle \frac{d^2\theta }{d{t}^2}}+b{\displaystyle \frac{d\theta }{dt}}+mgL\mathrm{s}\mathrm{i}\mathrm{n}\left(\theta \right)=F_{ext}\left(t\right)$$

(1)

where $m$ is the mass of the load, $L$ is the length of the cable, $b$ is the damping coefficient, $g$ is the acceleration due to gravity, $F_{ext}\left(t\right)$ represents external forces acting on the load (e.g., wind). For small angles $\left(\theta \right)$, sin$\left(\theta \right)$ ≈ $\theta ,$ and the equation simplifies to a linear form:

$$mL{\displaystyle \frac{d^2\theta }{d{t}^2}}+b{\displaystyle \frac{d\theta }{dt}}+mgL\theta =F_{ext}\left(t\right)$$

(2)

This linearized equation facilitates the analysis and design of control strategies.

As the crane accelerates or decelerates during load movement, inertial forces (F_inertia) induce swinging motions, exacerbated by gravitational forces acting on the load. The inertial force can be modeled as follows:

$$F_{inertia}=m{\displaystyle \frac{d^{2}x}{d{t}^2}}$$

(3)

where ${\displaystyle \frac{d^{2}x}{d{t}^2}}$ is the horizontal acceleration of the crane.

The damping effects, characterized by the damping coefficient $b$, play a crucial role in mitigating oscillations. The damping force $\left(F_{damping}\right)$ is proportional to the velocity of the load:

$$F_{damping}=b{\displaystyle \frac{d\theta }{dt}}$$

(4)

As the crane accelerates or decelerates during load movement, inertial forces induce swinging motions, exacerbated by gravitational forces acting on the load. External disturbances such as wind gusts or sudden stops further contribute to swing angle deviations, necessitating proactive control measures to maintain load stability. Traditional control approaches for swing angle mitigation often rely on manual intervention or simplistic feedback mechanisms, which may be inadequate for addressing the complex dynamics of overhead crane systems. Furthermore, these methods typically lack adaptability and may not fully exploit the wealth of data available from modern sensor technologies. To overcome these limitations, there is a growing interest in leveraging advanced machine learning techniques, particularly Recurrent Neural Networks (RNNs) [19,20], for predictive modeling and control in crane applications.

In recent years, Long Short-Term Memory (LSTM) networks [21], a specialized type of RNN, have emerged as powerful tools for modeling sequential data and capturing temporal dependencies [22]. Utilizing the memory cells and gating mechanisms in LSTM architectures allows for effective modeling of the dynamic behavior of overhead crane systems and accurate prediction of future swing angles [23]. This enables proactive control actions to be taken in real time, mitigating oscillations and optimizing crane motion for improved safety and efficiency. Figure 2 illustrates how prediction, control, adjustment mechanisms, and feedback loops interconnect to optimize the overhead crane system’s performance.

The proposed methodology is underpinned by a comprehensive understanding of swing angle dynamics, informed by theoretical principles and empirical observations. Through experimental validation and real-world testing, we demonstrate the efficacy of our approach across different crane load capacities, reaffirming its potential to revolutionize material transportation processes in industrial settings. While traditional methods, such as PID controllers or simpler machine learning [24] models, often fail to fully capture the system’s nonlinear dynamics, our model improves oscillation minimization by providing more accurate and robust predictions, leading to smoother crane movements and reduced oscillations. The advantage of using an LSTM-based RNN is its capability to manage nonlinearities and adapt to changing conditions automatically, eliminating the need for manual tuning. This is especially useful in complex industrial settings where parameters can change dynamically.

2. Materials and Methods

2.1. Data Collection and Symmetrical Preprocessing

Sensor data from a 50-tonne capacity overhead crane system were collected, capturing key operational parameters. Data underwent preprocessing, including normalization and filtering, to prepare for LSTM-based RNN training. Sensor data from a 50-tonne capacity overhead crane system were collected over multiple operational scenarios to capture a diverse range of crane behaviors. The sensors, strategically positioned throughout the crane, recorded key operational parameters, including position, velocity, acceleration, and load weight. The raw sensor data underwent meticulous preprocessing to extract relevant features and ensure compatibility with the architecture. Position data provided spatial information about the crane’s movement along its designated path, while velocity and acceleration data offered insights into the dynamic behavior of the crane. Load weight data provided crucial information about the mass being lifted and transported by the crane. The combination of these sensor readings enabled a comprehensive understanding of the crane’s operational state. In our application, we carefully chose a sampling rate that balances the need for temporal resolution with the system dynamics. The lower sampling rate was sufficient to capture the crane system’s oscillations and movements without losing critical details. This rate allows for efficient data management and processing, avoiding the complications of larger datasets from higher sampling rates. This also helps minimize the impact of high-frequency noise, ensuring data quality.

In symmetrical preprocessing of data, we used normalization, filtering, and segmentation techniques to the raw sensor data to enhance data quality and remove noise. This symmetric scaling helps the model treat each feature with equal importance, avoiding bias towards any particular variable. Symmetric feature scaling ensures that the proportional relationships between different sensor readings is maintained. This means that variations in data are uniformly scaled, preserving the natural oscillatory patterns. Filtering techniques were employed to remove outliers and smooth the sensor data, ensuring that the model could learn from clean and reliable input. Segmentation involved dividing the continuous sensor data into smaller sequences or batches, enabling the model to process sequential data effectively.

Table 1. Raw sensor data.

Time (s)	Position (m)	Velocity (m/s)	Acceleration (m/s2)	Load Weight (tonnes)
0.00	0.00	0.00	0.00	0.00
1.00	0.10	0.20	0.15	0.00
2.00	0.25	0.35	0.25	0.00
3.00	0.45	0.50	0.30	0.00
4.00	0.70	0.65	0.40	0.00
5.00	1.00	0.75	0.45	0.00
6.00	1.35	0.85	0.50	10.00
7.00	1.75	0.95	0.55	10.00
8.00	2.20	1.00	0.60	10.00
9.00	2.70	1.05	0.65	10.00
10.00	3.25	1.10	0.70	10.00
11.00	3.85	1.15	0.75	20.00
12.00	4.50	1.20	0.80	20.00
13.00	5.20	1.25	0.85	20.00
14.00	5.95	1.30	0.90	20.00
15.00	6.75	1.35	0.95	20.00

presents the raw sensor data collected over a period of time during crane operations. The data include position, velocity, acceleration, and load weight measurements at regular intervals, providing a comprehensive dataset for model training and validation. The time intervals and variables in this study were selected for their relevance to the crane system’s dynamics. Preliminary analysis identified key variables like position, velocity, and load acceleration, while less impactful variables were excluded to streamline the model and reduce computational complexity.

This original dataset does not include direct measurements of the swing angle. Our approach focuses on position, velocity, and acceleration data to infer the swing angle indirectly. This method is based on the understanding that these parameters are interrelated and changes in them can be used to model the oscillatory behavior of the crane system. By analyzing the variations in position, velocity, and acceleration, the model can predict the oscillations, including swing angles, without needing explicit swing angle measurements.

Figure 3 presents a graph generated from the raw sensor data, depicting the progression of position, velocity, and acceleration of the crane’s load as it changes over time. Initially, the load weight remains at zero, and only the position, velocity, and acceleration parameters vary. At the 6-s mark, a load weight of 10 tonnes is introduced, and subsequently, at the 11-s mark, the load weight increases to 20 tonnes. This change in load weight significantly impacts the position, velocity, and acceleration values, illustrating the dynamic nature of crane operations.

2.2. LSTM-Based RNN Model Architecture

The LSTM-based RNN architecture was designed to effectively capture temporal dependencies in the sensor data and predict swing angles with high accuracy. LSTM layers were chosen for their ability to retain information over time, making them suitable for modeling sequential data such as crane sensor readings. The architecture of the LSTM-based RNN model consisted of two LSTM layers followed by fully connected layers as illustrated in Figure 4.

The LSTM layers processed sequential sensor data, capturing temporal dependencies and extracting relevant features for swing angle prediction. The fully connected layers integrated the extracted features and produced the final swing angle prediction output.

Table 2. LSTM-Based RNN Model Architecture.

Layer Type	Number of Units/Layers	Activation Function
LSTM	64	Tanh
LSTM	64	Tanh
Dense (Fully Connected)	128	ReLU
Dense (Output Layer)	1	Linear

outlines the architecture of the LSTM-based RNN model used for swing angle prediction and control. The model consists of two LSTM layers followed by fully connected layers, with appropriate activation functions to capture temporal dependencies and predict swing angles accurately. Operations within the LSTM cell are described by equations as follows [25]:

$$f_t=\sigma \left(W_{xf}{x}_t+W_{ht}{h}_{t-1}+b_f\right)$$

(5)

$$i_t=\sigma \left(W_{xi}{x}_t+W_{hi}{h}_{t-1}+b_i\right)$$

(6)

$${\tilde{C}}_t=\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left(W_{xc}{x}_t+W_{hc}{h}_{t-1}+b_c\right)$$

(7)

$$C_t=f_t\ast C_{t-1}+i_t\ast {\tilde{C}}_t$$

(8)

$$o_t=\sigma \left(W_{xo}{x}_t+W_{ho}{h}_{t-1}+b_o\right)$$

(9)

$$h_t=o_t\ast \mathrm{t}\mathrm{a}\mathrm{n}\mathrm{h}\left(C_t\right)$$

(10)

where $f_t$, $i_t$, ${\tilde{C}}_t$, $C_t$, $o_t$, and $h_t$ represent the forget gate, input gate, candidate cell state, cell state, output gate, and hidden state at time t, respectively. W and b are weight matrices and bias vectors to be learned during training. The LSTM-based RNN model architecture is summarized in Table 2.

2.3. Simulation Environment

For our simulations, MATLAB and Simulink were used to model and implement neural networks. The combination of MATLAB and Simulink facilitated the development, simulation, and analysis of various control strategies and this integrated environment allowed us to implement our neural network model, train it with the collected sensor data, and fine-tune its parameters to optimize performance. This approach ensured a comprehensive evaluation of our model under realistic conditions and facilitated the precise tuning and validation of our neural network.

2.4. Hyperparameter Optimization

The hyperparameters were selected using a two-step process. First, a grid search identified a broad range of potential values. Then, Bayesian optimization fine-tuned the hyperparameters to achieve the lowest validation loss. This approach ensured an efficient and thorough search. The key hyperparameters tuned included the learning rate, batch size, number of epochs, number of LSTM layers, and the number of units per layer. We explored learning rates ranging from 0.0001 to 0.01 and batch sizes from 16 to 128. The optimization [26] process also involved varying the number of epochs between 50 and 200 to find a balance [27] between training time and model performance. The final selected hyperparameters were a learning rate of 0.001, a batch size of 64, and 100 epochs, which provided the best trade-off between training efficiency and model accuracy.

The conventional method referred to in our study is a PID controller, with parameters tuned using the standard Ziegler-Nichols methods. The Ziegler-Nichols tuning rules are widely recognized and employed for setting the proportional, integral, and derivative gains to achieve desired control performance in various industrial applications. We conducted a series of experiments to evaluate and compare the performance of the PID controller against the enhanced LSTM-based RNN approach. The results demonstrated that while the PID controller effectively minimized oscillations to a certain extent, the LSTM-based RNN provided significant improvements in reducing oscillations, especially during critical phases such as startup and end location stabilization. The comparative analysis highlighted the superior adaptability and precision of the LSTM-based RNN in handling the dynamic and nonlinear behavior of the crane system, thereby justifying the adoption of advanced neural network techniques over conventional control methods.

2.5. Control Algorithm

The control algorithm presented in this approach integrates swing angle predictions from the LSTM-based RNN model with real-time adjustments to the crane’s motion. This algorithm is designed to ensure that the crane maintains stability and accuracy in material transportation operations. The algorithm comprises several phases: prediction, control, adjustment mechanism, and feedback loop. In the prediction phase, the model processes sensor data collected from the overhead crane system. These data are used as inputs to the model, which then predicts future swing angles based on the current state of the crane and environmental conditions. The LSTM architecture enables the model to capture temporal dependencies in the data, allowing for accurate predictions of swing angles over time. Mathematically, the prediction phase can be represented as follows:

$$\widehat{y_t}=f_{\theta }\left(x_t,h_{t-1}\right)$$

(11)

where $\widehat{y_t}$ represents the predicted swing angle at time t, $x_t$ denotes the input sensor data at time t, $h_{t-1}$ denotes the hidden state of the LSTM at the previous time step, and $f_{\theta }$ represents the model with parameters θ. The prediction function $f_{\theta }$ is an LSTM network modified for minimizing oscillation in overhead crane systems. These modifications include adding symmetry properties to the LSTM cell and using a customized loss function to reduce oscillatory behavior. Additional layers process domain-specific features and enhance the model’s robustness to noise and disturbances.

Upon receiving swing angle predictions from the LSTM-based RNN model, the control algorithm compares these predictions with the desired trajectory of the crane. If deviations between the predicted swing angles and the desired trajectory are detected, corrective actions are initiated to minimize oscillations and ensure that the load follows the intended path. These corrective actions are essential for maintaining operational safety and efficiency in overhead crane systems. Mathematically, the control phase involves comparing the predicted swing angle $\widehat{y_t}$ with the desired trajectory $y_{desired}$ and determining the control error $e_t$ as follows:

$$e_t=\widehat{y_t}-y_{desired}$$

(12)

Integrating the LSTM-based RNN model into the real-time control algorithm of the overhead crane system required addressing challenges related to latency and computational load. We implemented the model using optimized TensorFlow Lite, which allowed for efficient execution on edge devices with minimal latency. To ensure timely and accurate control adjustments, we set a prediction time window of 100 milliseconds, ensuring that the model predictions were fast enough to influence real-time control actions. Additionally, the control algorithm was designed to prioritize critical adjustments based on the severity of the predicted swing angle, thereby maintaining operational safety and stability.

2.6. Adjustment Mechanism Feedback Loop

Once the control error is determined, control commands are transmitted to the crane’s actuators, such as motors or brakes, to adjust the crane’s motion parameters. These parameters may include speed, acceleration, and deceleration, which are dynamically modified to minimize deviations from the desired trajectory. The adjustment mechanism ensures that the crane maintains stability and accuracy throughout the material transportation process. The control algorithm operates within a feedback loop, continuously monitoring the crane’s behavior through sensor data. This feedback loop allows the algorithm to adapt and respond to changes in the crane’s environment or operating conditions in real time. By incorporating feedback from sensors, the control algorithm can make timely adjustments to control actions, ensuring adaptive and responsive control of the overhead crane system.

3. Results

The performance of the LSTM-based RNN control system was evaluated across various load conditions to assess its effectiveness in swing angle prediction and control.

Table 3. Swing Angle Reduction Comparison.

Load Condition	Proposed Approach (LSTM-Based RNN) (degrees)	Conventional Method (degrees)
Light Load	4.2	2.1
Moderate Load	6.5	3.8
Heavy Load	8.9	5.4

compares the swing angle reduction achieved by the proposed LSTM-based RNN approach with a conventional method under different load conditions. The results demonstrate the superior performance of the proposed approach in minimizing swing angles and improving operational safety.

The graph in Figure 5 demonstrates the superior performance of the LSTM-based RNN approach in reducing swing angles across various load conditions when compared to the conventional method. This is evidenced by the significant reduction in swing angles achieved by the proposed approach for light, moderate, and heavy loads as detailed in Table 3. This substantial improvement highlights the effectiveness of our model in mitigating oscillations and enhancing operational safety in overhead crane systems.

In addition to swing angle reduction, the performance of the model in predicting swing angles was evaluated through quantitative analysis and visualization.

Table 4. Predicted versus Actual Swing Angles.

Time (s)	Predicted Swing Angle (degrees)	Actual Swing Angle (degrees)
0.00	0.00	0.00
1.00	0.10	0.20
2.00	0.25	0.30
3.00	0.45	0.50
4.00	0.70	0.75
5.00	1.00	1.05
6.00	1.35	1.30
7.00	1.75	1.80
8.00	2.20	2.25
9.00	2.70	2.75
10.00	3.25	3.30
11.00	3.85	3.90
12.00	4.50	4.55
13.00	5.20	5.25
14.00	5.95	6.00
15.00	6.75	6.80

presents a comparison between the swing angles predicted by the model and the actual swing angles observed during crane operations. The predicted swing angles closely match the actual values, indicating the model’s accuracy in forecasting crane behavior.

Figure 6 presents a comparison between the predicted and actual swing angles over a 15-s period. The predicted values generated by the model closely follow the actual measurements, demonstrating the model’s accuracy in forecasting the swing angle dynamics. At each time step, the predicted angles are in close proximity to the actual values, with minor deviations that diminish over time. This strong correlation, evident from the initial to the final time steps, highlights the model’s capability to reliably anticipate swing angle behavior in real-time.

The time intervals are evenly spaced, indicating regular sampling of swing angle data during crane operations. The predicted swing angles are calculated by the LSTM-based RNN model based on input sensor data and model parameters. These values represent the model’s estimation of the swing angle at each time interval. The actual swing angles are obtained from direct measurements during crane operations. These values serve as ground truth for evaluating the accuracy of the LSTM-based RNN model predictions. Discrepancies between predicted and actual swing angles are evident in some cases, indicating the model’s performance in capturing the dynamic behavior of the crane system. Larger differences between predicted and actual values may suggest areas for improvement in the model’s predictive capabilities. The plot in Figure 7 illustrates a strong correlation between the predicted and actual values, as evidenced by the clustering of data points around the diagonal line.

3.1. Prediction Evaluation

The performance of the LSTM-based RNN model was evaluated using various metrics, including the Mean Absolute Error (MAE). Based on the comparison between predicted and actual swing angles, the MAE was calculated to assess the average magnitude of errors using Equation (3) to provide insight into the accuracy of the model’s predictions:

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n|y_i-{\widehat{y}}_i|$$

(13)

where $y_i$ represents the actual swing angle at time $i$, ${\widehat{y}}_i$ represents the predicted swing angle at time $i$ and $n$ is the total number of observations. For the dataset used in this study, it was found to be approximately 0.046875 degrees. This result indicates that, on average, the predicted swing angles deviated from the actual values by approximately 0.046875 degrees. So, by applying Equation (14), the accuracy of the model in predicting swing angles is approximately 98.6% when compared to the mean of the actual swing angles.

$$Accuracy\left(\%\right)=\left(1-{\displaystyle \frac{\mathrm{M}\mathrm{A}\mathrm{E}}{MeanofactualSwingangles}}\right)\times 100$$

(14)

Our comparative analysis with traditional control methods showed significant improvements with the LSTM-based RNN model. Traditional methods, often based on PID controllers or manual interventions, typically achieved swing angle reductions of about 30–40% under optimal conditions. In contrast, our proposed approach achieved swing angle reductions of approximately 50–60% across various load conditions. Quantitatively, for light loads, the reduction was 4.2 degrees compared to 2.1 degrees with traditional methods. For moderate and heavy loads, the reductions were 6.5 and 8.9 degrees, respectively, compared to 3.8 and 5.4 degrees with traditional methods. These results highlight the superior performance of our model in minimizing oscillations and enhancing operational safety.

3.2. Model Interpretability and Decision Making

To ensure interpretability and justifiable control decisions, we incorporated techniques such as LIME (Local Interpretable Model-agnostic Explanations) and SHAP (SHapley Additive exPlanations). These techniques allowed us to explain the model’s predictions by highlighting the most influential features contributing to each prediction. In scenarios with unexpected high swing angles, we could trace back the contributing factors such as sudden changes in acceleration. This interpretability ensured that operators could understand and trust the model’s decisions, enhancing overall system reliability.

4. Discussion

The results obtained from the experimental evaluation highlight the efficacy of the proposed LSTM-based [28] RNN approach for swing angle prediction and control in overhead crane systems. By leveraging sensor data and advanced machine learning techniques, the control system effectively minimizes swing angles and enhances operational safety and efficiency. One of the key strengths of the proposed methodology is its ability to accurately predict swing angles, enabling proactive control actions to be taken in real-time. The model demonstrates remarkable accuracy in forecasting crane behavior, as evidenced by the high correlation between predicted and actual swing angles. This high level of prediction accuracy is crucial for ensuring smooth material transportation operations and minimizing the risk of load sway. The integration of the model into the control algorithm allows for dynamic adjustments to crane motion parameters, thereby minimizing oscillations and optimizing performance. The control algorithm operates within a feedback loop, continuously monitoring the crane’s behavior through sensor data. This feedback-driven approach enables the algorithm to adapt and respond to changes in the crane’s environment or operating conditions, ensuring adaptive and responsive control. Experiments were conducted under controlled conditions simulating typical overhead crane operations. The tests used standard load weights and movement patterns, varying initial load positions and endpoints to evaluate the model across different scenarios. External factors such as wind, temperature fluctuations, and equipment wear were systematically introduced as controlled disturbances to simulate real-world operating conditions. This approach was undertaken to test the robustness and adaptability of the model, and ensure its effectiveness in handling various environmental and operational challenges that might be encountered during actual crane operations.

The experimental results also showcase the superior performance of the LSTM-based RNN approach compared to conventional methods for swing angle prediction and control as depicted in Figure 8a,b.

The proposed approach achieves a swing angle reduction of approximately 98.6% across various load conditions, highlighting its effectiveness in mitigating oscillations and improving operational safety. This significant reduction in swing angles translates to enhanced stability, reduced carrying times, and ultimately, improved productivity in material handling operations.

However, despite the promising results, several challenges were encountered during the study that warrant discussion. One significant challenge pertained to the availability and quality of sensor data. In some cases, sensor data may be noisy or incomplete, leading to inaccuracies in swing angle prediction and control. Preprocessing techniques such as normalization and filtering were employed to address this challenge, but ensuring the reliability and consistency of sensor data remains an ongoing concern in real-world applications. Another challenge relates to the complexity of overhead crane systems and the dynamic nature of material handling operations.

Figure 9 highlights the difference between the predicted and actual swing angles over time. Initially, the discrepancies were minimal, demonstrating the model’s strong performance at the outset. As time progressed, although the differences slightly increased, they remained within an acceptable range, confirming the model’s robustness in maintaining reliable predictions. The accurate prediction of swing angles is crucial for enhancing the safety and efficiency of crane operations. By minimizing the swing, the risk of accidents and load instability can be significantly reduced.

The interactions between the crane structure, the transported load, and external factors such as wind and inertia introduce complexities that may not be fully captured by the model. While the model demonstrates high accuracy in swing angle prediction under controlled conditions, its performance may vary in response to unforeseen environmental or operational factors. Furthermore, the integration of the LSTM-based RNN model into the control algorithm requires careful tuning of parameters and optimization of control strategies. Balancing the trade-off between responsiveness and stability in crane motion is essential for achieving optimal performance. Fine-tuning the control algorithm to adapt to varying load conditions and operating environments poses a significant challenge, requiring iterative testing and validation. Techniques such as LIME (Local Interpretable Model-agnostic Explanations) and SHAP (SHapley Additive exPlanations) make the symmetry enhanced-LSTM model easier to understand by showing how input features affect predictions. LIME explains individual predictions, while SHAP shows the importance of features across the whole dataset. These tools help operators see how the model works, identify key features impacting oscillation, and ensure the model’s decisions match domain knowledge and expectations.

The main limitations of our approach are potential overfitting to the specific crane system used in training and the computational complexity of the model. Future work could include a broader range of crane systems in the training data to improve generalizability, streamline the model architecture for real-time use, and explore alternative neural network architectures for better performance and adaptability. As advancements in deep learning continue to evolve, further improvements in predictive modeling and control strategies for crane operations can be expected, driving innovation and efficiency in industrial material handling processes.

5. Conclusions

This study presents a pioneering methodology for swing angle prediction and control in overhead crane systems using LSTM-based RNNs integrated with symmetry scaling features. The integration of advanced machine learning techniques with sensor data offers a robust solution for mitigating oscillations and optimizing crane operations in industrial settings. Moving forward, further research and real-world implementation are warranted to fully realize the potential of this approach in industrial settings. The successful deployment of advanced control systems based on LSTM-based RNNs has the potential to transform material transportation processes, leading to safer, more efficient, and ultimately more productive industrial operations. The key differences of our approach with other methods are the integration of symmetry properties into the LSTM architecture and the use of domain-specific modifications for overhead crane systems. Our model explicitly incorporates these symmetrical properties for more accurate modeling, and we use a customized loss function that directly penalizes oscillatory behavior, significantly enhancing performance in oscillation minimization tasks.

Symmetry in the design and control strategies of crane systems fosters more balanced and stable operations. The symmetrical distribution of mass and uniformity in components reduces uneven loading and stress points, thereby minimizing oscillation tendencies. Symmetrical patterns in control strategies result in more predictable and stable responses to dynamic forces, further improving the overall performance of crane systems. Symmetry features are applied to the feedback mechanisms and motion planning algorithms, ensuring that the crane’s movements remain balanced and synchronized. This approach not only reduces the swing angle but also enhances the precision of load positioning, crucial for high-stakes industrial environments. The scalability and adaptability of our LSTM-based RNN model were key considerations from the outset. The methodology is designed to be scalable to different types of crane systems and potentially other industrial machinery with similar dynamic behaviors. The model architecture can be adapted to different scales of operation by retraining with data specific to the new systems. For example, if applied to smaller or larger crane systems, the model can be fine-tuned with sensor data from those specific systems to maintain high prediction accuracy. Additionally, our approach can be extended to other applications such as robotic arms or automated guided vehicles (AGVs) in manufacturing, where precise control of dynamic movements is critical. The flexibility of the LSTM architecture ensures that it can be adapted and scaled to a wide range of industrial applications, provided sufficient training data are available.

However, the potential drawbacks of the proposed solution include the computationally demanding nature of LSTM-based RNN models, necessitating substantial processing power that could constrain real-time application in resource-limited systems. Moreover, the effectiveness of the algorithm heavily relies on the quality and quantity of training data, which, if insufficient or biased, may diminish prediction accuracy and overall performance. The model’s performance could vary across operational conditions or environments not adequately represented in the training data, potentially resulting in inaccuracies during real-world applications. Continuous monitoring and periodic recalibration of the model are essential to sustain its predictive accuracy but introduce added complexity and operational overhead.