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The least-squares method is one of the most efficient and simple identification methods commonly used. Unfortunately, it is very sensitive to large errors (outliers) in the input/output data. In such cases, it may never converge or give erroneous results. In earlier work, based on the minimax principle, a robust least-squares version has been proposed, but it is only suitable for linear systems. In practice, most real systems are nonlinear. Many of these can be suitably represented by bilinear models. In the paper, a robust recursive least-squares method has been proposed for bilinear system identification. It differs from earlier approaches in that it uses modified weights in the criterion for robustness. A theorem proving the convergence of the proposed algorithm is included. Results of the simulation demonstrating the robustness of the proposed algorithm are also included.

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Thermal errors are one of the most significant factors that influence the machining precision of machine tools. For large-sized gear grinding machine tools, thermal errors of beds, columns and rotary tables are decreased by their huge heat capacity. However, different from machine tools of normal sizes, thermal errors increase with greater power in motorised spindles. Thermal error compensation is generally considered as a relatively effective, convenient and cost-efficient approach in thermal error control and reduction. This article proposes two thermal error prediction models for motorised spindles based on an adaptive neuro-fuzzy inference system and support vector machine, respectively. In the adaptive neuro-fuzzy inference system–based model, the temperature values are divided into different groups using subtractive clustering. A hybrid learning scheme is adopted to adjust membership functions so as to learn from the input data. In the particle swarm optimisation support vector machine–based model, particle swarm optimisation is used to optimise the hyperparameters of the established model. Thermal balance experiments are conducted on a large-sized computer numerical control gear grinding machine tool to establish the prediction models. Comparative results show that the adaptive neuro-fuzzy inference system model has higher prediction accuracy (with residual errors within ±2.5 μm in the radial direction and ±3 μm in the axial direction) than the support vector machine model.