1 Introduction In the overall performance study of the engine, the accuracy of the engine component characteristics map has a significant impact on the overall performance calculations. Experience shows that if the component characteristics are not properly selected, the matching work points in the engine are often not obtained in some operating conditions. In the whole machine test, the accurate component characteristics are also important for the monitoring of engine performance and fault diagnosis. When performing research, analysis and monitoring of a functioning engine that has been put into operation, due to changes in the mathematical model of the component characteristics or the theoretical and random errors in the measurement device itself, as well as the installation impact of various components and the working environment, etc. The actual characteristics of the engine components are not completely consistent with those calculated or tested by the components. Therefore, it is necessary to infer the characteristics of the components that are close to the actual operation from the limited engine known performance data. The coupling coefficient of the engine performance is used to calculate the correction coefficient of the relevant component characteristics, and the correction factor is used to modify the original characteristics.
The coupling optimization calculation method is more mature, but when used for component modification, a simple approximation is generally used. In this paper, the coupled optimization of engine steady-state performance is used to calculate the coupling coefficient of the component characteristics at each operating point. The non-linear least-squares fitting based on the similarity of the characteristic diagram is used to modify the characteristic surface of the engine to obtain more Close to the actual operating conditions of the component characteristics.
Since the samples can be arbitrarily distributed on the map, this article uses the form of a surface to describe the characteristics of the part. If there are a large number of sample data distributed over the entire characteristic range, the first and second derivatives of the surface can be directly estimated using these discrete data points and a smooth characteristic surface can be fitted. However, it is usually difficult to obtain enough. The data points, therefore, must be corrected by referring to the variation of the original characteristic diagram. Based on the similarity of the change rule of the same type of component property map, in the correction calculation, the node value of the characteristic surface grid is used as an independent variable when the surface is fitted; the first, second and mixed derivatives of the node are used as optimization objectives. In part, the variation of the surface of the original features is basically maintained. Curve fitting, using a non-linear least-squares method, so that the characteristic values ​​of each sample point, in the least-squares sense, are sufficiently close to the value obtained by the coupling optimization calculation (equal to the product of the coupling coefficient and the reference characteristic value). In this way, the modified characteristic can better conform to the actual characteristics, and it can also better maintain the variation of the characteristic surface.
Due to the use of local bicubic interpolation at the sample point, one sample value only affects the correction of the adjacent 16 nodes. In order to increase the calculation speed, the characteristic region is divided into a sample-containing portion and a non-sample-containing portion. The non-linear least-squares fitting of the component characteristic diagram is corrected in these two domains, and the iteration is performed in turn to perform the nonlinear minimum. Two times fit until it meets the accuracy requirements. With the above method, the total error level of each sample can be minimized in the least squares sense. When verifying the accuracy of the corrected component characteristics, the engine performance coupling optimization algorithm is also used. From the definition of the coupling coefficient, it can be seen that if the corrected characteristic calculation is used, the closer the coupling coefficient is to 1, the better the consistency with the true characteristic is.
4 Calculation results The combustion chamber efficiency characteristics are used as an example.
In order to facilitate the observation of the change, the coupling coefficient of each sample point before characteristic correction is drawn in ascending order, and the correction coefficient of each point after characteristic correction is drawn in the order of these points. As can be seen from Fig.1, after the characteristics are corrected, the correction coefficients of each sample point are concentrated in the vicinity of 1.0, especially the point where the original deviation is large has been greatly improved. Since in the property correction, the total error level of all the samples tends to be the smallest, some of the original correction coefficients close to 1.0 will not have a large tendency to deviate. This aspect is due to the impact of other points, but also related to the accuracy of the steady-state mathematical model.
5 Conclusions Using a nonlinear least-squares fitting algorithm based on the similarity of similar components' characteristics, it is possible to obtain a characteristic map that more closely matches the actual characteristics of the components from the modified coefficients of the discrete samples. The algorithm is feasible and effective. The revised component characteristic diagram can more accurately reflect the actual operating characteristics, the accuracy of the result and the closeness of the engine's steady state model to the actual operating conditions (such as the accuracy of the algorithm, the actual working conditions and the accuracy of the process simulation, etc. ), the amount of raw data and its accuracy and other factors are closely related. In addition, a detailed mathematical description of the characteristics of each component should be carried out, such as its change law and scope of change, etc., and these characteristics should be fully taken into account when implementing a nonlinear least-squares fitting algorithm, so that the modified characteristic map can be better Reflect the real characteristics of the component characteristics.
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