Nikolaus Rudak

Joint optimization of independent multiple responses

Most of the existing methods for the analysis and optimization of multiple responses require some kinds of weighting of these responses, for instance in terms of cost or desirability. Particularly at the design stage, such information is hardly available or will rather be subjective. An alternative strategy uses loss functions and a penalty matrix that can be decomposed into a standardizing (data-driven) and a weight matrix. The effect of different weight matrices is displayed in joint optimization plots in terms of predicted means and variances of the response variables. In this article, we propose how to choose weight matrices for two and more responses. Furthermore, we prove the Pareto optimality of every point that minimizes the conditional mean of the loss function. Copyright

On- and offline detection of structural breaks in thermal spraying processes

We investigate and develop methods for structural break detection, considering time series from thermal spraying process monitoring. Since engineers induce technical malfunctions during the processes, the time series exhibit structural breaks at known time points, giving us valuable information to conduct the investigations. First, we consider a recently developed robust online (also real-time) filtering (i.e. smoothing) procedure that comprises a test for local linearity. This test rejects when jumps and trend changes are present, so that it can also be useful to detect such structural breaks online. Second, based on the filtering procedure we develop a robust method for the online detection of ongoing trends. We investigate these two methods as to the online detection of structural breaks by simulations and applications to the time series from the manipulated spraying processes. Third, we consider a recently developed fluctuation test for constant variances that can be applied offline, i.e. after the whole time series has been observed, to control the spraying results. Since this test is not reliable when jumps are present in the time series, we suggest data transformation based on filtering and demonstrate that this transformation makes the test applicable.

Simultaneous Optimization of Multiple Correlated Responses with Application to a Thermal Spraying Process

In industrial applications, it is often desired to find settings of process parameters, which lead to pre-specified target values of multiple quality characteristics with minimal variance. One approach to solve this problem is to minimize an estimated risk function depending on a cost matrix. The joint optimization (JOP) method follows this general strategy using a sequence of diagonal cost matrices and requires estimated models for the expectation and the variance of the responses. However, if the quality characteristics might be correlated, this should be considered at the model or optimization stage in order to find a realistic solution. In this contribution, we extend the JOP method to the simultaneous optimization of correlated multiple responses. We also introduce a new approach for the choice of non-diagonal cost matrices. The resulting JOP method for correlated responses is illustrated on an application arising in the field of thermal spraying. Copyright

Joint optimization of multiple responses based on loss functions

Most of the existing methods for the analysis and optimization of multiple responses require some kind of weighting of these responses, for instance in terms of cost or desirability. Particularly at the design stage, such information is hardly available or will rather be subjective. Kuhnt and Erdbrügge (2004) present an alternative strategy using loss functions and a penalty matrix which can be decomposed into a standardizing (data-driven) and a weight matrix. The effect of different weight matrices is displayed in joint optimization plots in terms of predicted means and variances of the response variables. In this article, we propose how to choose weight matrices for two and more responses. Furthermore we prove the Pareto optimality of every point that minimizes the conditional mean of the loss function.