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In this article, a phase-shifting fault-tolerant control (PS-FTC) method with single-phase current sensor is proposed for primary permanent-magnet linear motor traction system. The phase with healthy sensor is defined as the first phase, while the other two phases without healthy sensors are, respectively, defined as the second and third phases. In PS-FTC, hysteresis current control is adopted. The actual currents of the second and third phases are replaced by the estimated values, while the reference values are obtained by phase shifting of the estimated first-phase current. Although the linear motor parameters have been used in the calculation of the estimated currents, the parameter variations do not affect the performances of PS-FTC. Compared with the conventional fault-tolerant control (C-FTC) method and the existing fault-tolerant control schemes with single-phase current sensor, PS-FTC is robust and shows better steady-state performances. Furthermore, a hybrid strategy combining PS-FTC and C-FTC is adopted to improve the transient-state performances. The effectiveness of PS-FTC and the hybrid strategy are verified by the theoretical analysis and experimental results. [ABSTRACT FROM AUTHOR]

We present a novel chi-squared progressive photon mapping algorithm (CPPM) that constructs an estimator by controlling the bandwidth to obtain superior image quality. Our estimator has parametric statistical advantages over prior nonparametric methods. First, we show that when a probability density function of the photon distribution is subject to uniform distribution, the radiance estimation is unbiased under certain assumptions. Next, the local photon distribution is evaluated via a chi-squared test to determine whether the photons follow the hypothesized distribution (uniform distribution) or not. If the statistical test deems that the photons inside the bandwidth are uniformly distributed, bandwidth reduction should be suspended. Finally, we present a pipeline with a bandwidth retention and conditional reduction scheme according to the test results. This pipeline not only accumulates sufficient photons for a reliable chi-squared test, but also guarantees that the estimate converges to the correct solution under our assumptions. We evaluate our method on various benchmarks and observe significant improvement in the running time and rendering quality in terms of mean squared error over prior progressive photon mapping methods. [ABSTRACT FROM AUTHOR]