How do you evaluate the performance and robustness of different thruster allocation algorithms?

1 What is a TA algorithm?

A TA algorithm is a mathematical procedure that calculates the optimal or near-optimal commands for each thruster, given the desired forces and moments from the DP controller and the operational and physical limits of the thrusters. A TA algorithm can be based on different principles, such as linear programming, quadratic programming, genetic algorithms, artificial neural networks, or fuzzy logic. The main objectives of a TA algorithm are to minimize the power consumption, the wear and tear, and the noise of the thrusters, while ensuring the feasibility and stability of the solution.

2 How to measure the performance of a TA algorithm?

When measuring the performance of a TA algorithm, criteria will vary depending on the application and goals of the DP system. Accuracy is the difference between the desired and actual forces and moments produced by thrusters, while efficiency is the ratio between power consumption and the magnitude of these forces and moments. Smoothness is the degree of variation or fluctuation of thruster commands over time, and robustness is the algorithm's ability to handle uncertainties, disturbances, and faults in the DP system.

3 How to test the robustness of a TA algorithm?

The robustness of a TA algorithm can be tested by exposing it to different scenarios that may affect the DP system, such as changes in environmental conditions, vessel dynamics, thruster characteristics, or sensor/actuator/communication malfunctions. To evaluate its robustness, one should measure how well it can cope with these scenarios without compromising accuracy, efficiency, or smoothness. Metrics such as the frequency and severity of constraint violations, thruster switching, redundancy, and performance degradation can help assess the algorithm's robustness.

4 How to compare different TA algorithms?

To compare different TA algorithms fairly and consistently, it is essential to apply representative test cases of real-world situations that the DP system may encounter. This should include a range of operational modes, environmental conditions, and fault scenarios. The same parameters, constraints, and objectives should be used for each TA algorithm on the same DP system model. Additionally, the test cases should be repeated enough times to obtain statistically significant results and account for any randomness or variability associated with certain TA algorithms. Lastly, performance and robustness indicators should be defined and quantified with appropriate units, scales, and normalization methods.

5 What are some examples of TA algorithms?

There are many TA algorithms that have been developed and applied for different types of DP systems and vessels, such as the pseudo-inverse method, the weighted pseudo-inverse method, the quadratic programming method, the genetic algorithm method, and the artificial neural network method. The pseudo-inverse method is a simple and fast linear algorithm that uses the Moore-Penrose pseudo-inverse matrix to solve the TA problem. The weighted pseudo-inverse method is a modified version that introduces weighting factors to account for thruster efficiency and redundancy. The quadratic programming method is a nonlinear algorithm that uses an optimization technique to minimize a quadratic cost function that reflects power consumption and smoothness of the TA solution. The genetic algorithm method is a stochastic algorithm that uses an evolutionary approach to find the optimal or near-optimal TA solution. Lastly, the artificial neural network method is a learning algorithm that uses a network of artificial neurons to approximate the nonlinear mapping between desired forces and moments and thruster commands.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?