The above life prediction work was mainly based on FE simulations to obtain stress and strain. Accurate modeling of the injection process is the first step for short-term failure or fatigue analysis [,,,]Simla Stock. However, FE simulation is generally based on deterministic parameters in an ideal state, so there are always errors compared with the actual situation. These errors and uncertainties are very important reasons explaining the fluctuation in the injection processAhmedabad Stock. For thermal fatigue analysis of a shot sleeve, temperature plays a direct role [], which includes the pouring temperature and the preheating temperature of the shot sleeve. When molten metal is poured from a crucible into a shot sleeve, there will be temperature loss. There are also many uncertain factors such as inaccurate temperature measurement and uneven preheating temperature in the preheating process of a shot sleeve. However, in an FE simulation, these parameters are assumed to be definite values, which will inevitably lead to errors between the simulation and the experiment. Therefore, life prediction based on a deterministic simulation will inevitably have errors, which will directly determine the accuracy of the life prediction, and it is necessary to analyze these uncertain factors in order to achieve thermal fatigue life prediction with higher reliability []. Monte Carlo simulation (MCS) is one of the most commonly used methods in uncertainty analysis [,]. Its basic principle is to draw (pseudo-) random numbers from a set of input parameters with known distribution functions to obtain a sampled distribution of the output parameter. However, MCS requires a large number of sample points for simulation, and it is inefficient to obtain data only by FE simulation. Therefore, a Kriging surrogate model is used to approximate the FE model. The surrogate model usually refers to an approximate mathematical model that can be used to replace complex and time-consuming numerical models (e.g., FE models) in analysis and optimization design. Here, the term “surrogate model” has the same meaning as “response surface model”, “metamodel”, “approximation model”, “emulator”, etc. []. The Kriging model is an optimal unbiased estimation model that uses the known information of sample points near an unknown point to estimate the unknown point by linear weighting [,]. The Kriging model has been widely used in uncertainty modeling and parameter optimization because of its good approximation ability to nonlinear responses and useful estimation of error. For example, Gao et alChennai Stock. [] utilized an MCS to generate random samples and a Kriging surrogate model to approximate a high-order flow field calculation model and successfully analyzed the influence of a blade machining error on compressor performance. Ma et alVaranasi Investment. [] proposed an optimization method to obtain optimal electrical discharge machining (EDM) parameters. In their study, a Kriging model was built to approximate the relationship between the EDM parameters and the machining accuracy. The constraint function was the probability that the aperture gap calculated by MCS was lower than the given value. Sun et al. [] proposed a prediction method of mechanism dynamic wear with aleatory and epistemic uncertainty. The Kriging model was applied to replace the simulated model of wear prediction, and the Improved Double-Loop Monte Carlo Sampling Approach was used to propagate the influence of parameter uncertainty on the system response in the whole time domain. You et al. [] established a spatiotemporal Kriging model to substitute the complicated computer model, which could accurately predict the temperature at different positions of the shot sleeve, but their research did not involve parameter uncertainty.
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