The performance of a six-axis force/torque sensor (F/T sensor) severely decreased when working in an extreme environment due to its sensitivity to ambient temperature. This paper puts forward an ensemble temperature compensation method based on the whale optimization algorithm (WOA) tuning the least-square support vector machine (LSSVM) and trimmed bagging. To be specific, the stimulated annealing algorithm (SA) was hybridized to the WOA to solve the local entrapment problem, and an adaptive trimming strategy is proposed to obtain the optimal trim portion for the trimmed bagging. In addition, inverse quote error (invQE) and cross-validation are employed to estimate the fitness better in training process. The maximum absolute measurement error caused by temperature decreased from $3.34\%$ to $3.9\times {10}^{-3}\%$ of full scale after being compensated by the proposed method. The analyses of experiments illustrate the ensemble hWOA-LSSVM based on improved trimmed bagging improves the precision and stability of F/T sensors and possesses the strengths of local search ability and better adaptability.

Six-axis force/torque sensors are widely installed in manipulators to help researchers achieve closed-loop control. When manipulators work in comic space and deep sea, the adverse ambient environment will cause various degrees of damage to F/T sensors. If the disability of one or two dimensions is restored by self-restoration methods, the robustness and practicality of F/T sensors can be considerably enhanced. The coupling effect is an important characteristic of multi-axis F/T sensors, which implies that all dimensions of F/T sensors will influence each other. We can use this phenomenon to speculate the broken dimension by other regular dimensions. Back propagation neural network (BPNN) is a classical feedforward neural network, which consists of several layers and adopts the back-propagation algorithm to train networks. Hyperparameters of BPNN cannot be updated by training, but they impact the network performance directly. Hence, the particle swarm optimization (PSO) algorithm is adopted to tune the hyperparameters of BPNN. In this work, each dimension of a six-axis F/T sensor is regarded as an element in the input vector, and the relationships among six dimensions can be obtained using optimized BPNN. The average MSE of restoring one dimension and two dimensions over the testing data is $1.1693\times {10}^{-5}$ and $3.4205\times {10}^{-5}$, respectively. Furthermore, the average quote error of one restored dimension and two restored dimensions are $8.800{\times 10}^{-3}$ and $8.200{\times 10}^{-3}$, respectively. The analysis of experimental results illustrates that the proposed fault restoration method based on PSO-BPNN is viable and practical. The F/T sensor restored using the proposed method can reach the original measurement precision.

The wind tunnel balance signal detection system is widely employed in aerospace applications for the accurate and automated measurement of aerodynamic forces and moments. However, measurement errors arise under different environmental temperature. This paper addresses the issue of measurement accuracy under different temperature conditions by proposing a temperature compensation method based on an improved gray wolf optimization (IGWO) algorithm and optimized extreme learning machine (ELM). The IGWO algorithm is enhanced by improving the initial population position, convergence factor, and iteration weights of the gray wolf optimization algorithm. Subsequently, the IGWO algorithm is employed to determine the optimal network parameters for the ELM. The calibration decoupling experiment and high-low temperature experiment are designed and carried out. On this basis, ELM, GWO-ELM, PSO-ELM, GWO-RBFNN and IGWO-ELM are used for temperature compensation experiments. The experimental results show that IGWO-ELM has a good temperature compensation effect, reducing the measurement error from 20${\%}_{FS}$ to within 0.04${\%}_{FS}$. Consequently, the accuracy and stability of the wind tunnel balance signal detection system under different temperature environments are enhanced.