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Most of the existing steady state detection approaches are designed for univariate signals. For multivariate signals, the univariate approach is often applied to each process variable and the system is claimed to be steady once all signals are steady, which is computationally inefficient and also not accurate. The article proposes an efficient online method for multivariate steady state detection. It estimates the covariance matrices using two different approaches, namely, the mean-squared-deviation and mean-squared-successive-difference. To avoid the usage of a moving window, the process means and the two covariance matrices are calculated recursively through exponentially weighted moving average. A likelihood ratio test is developed to compare the difference of the two covariance matrices and to detect the steady state. The intensive numerical studies and real case study show that the proposed method can accurately detect the steady state of a multivariate system. INTRODUCTION Detecting if a system or a process is steady is a significantly important task in many engineering problems, such as process analysis and optimization [1-4], fault detection and diagnosis [5, 6], data reconciliation [7, 8], process automation and control [911]. In these applications, the steady state is often defined as a state where the mean of the time series stays unchanging. For example, in the chemical industry, process data (e.g., flow rate, pH values, temperature etc.) have to be collected under steadystate conditions for unit design, pinch analysis, process optimization, and fault detection [12]. Besides, almost all the fault detection and diagnostic (FDD) methodologies are based on steady state models and require that the system is steady [6, 13]. Another example is batch process or batch manufacturing. During batch-to-batch start-up periods, the batch operations are not steady at the beginning due to that the materials are not mixed well and the machine conditions such as temperature and pressure are not stable, which cannot guarantee the product quality [14, 15]. Therefore, an efficient method for steady-state detection could help achieve satisfied products and avoid expensive quality inspection. In process automation and control, the steady state can be used to trigger the next action. For example, in ultrasonic cavitation based particle dispersion process, the steady state condition of the cavitation noise has been used as a process completion indicator [11]. Once the noise signal is steady state, the dispersion process is considered completed and the process can be stopped. In the numerical iterative methods, such as nonlinear regression, optimization and neural network training, the steady state condition can also be used as a stopping or convergence criterion. The iterative procedures will be stopped once the objective function like the sum of squared error reaches a steady state [9, 16]. Steady state detection applies various statistical techniques to identify the transition from nonstationary state (also called transient state, start-up or warm-up period) to the steady state. It should be noted that the traditional statistical process control techniques utilize various control charts to monitor the change from steady state to other steady or nonstationary states, which is opposite to the steady state detection. In the last few decades, there are more than forty offline steady-state detection algorithms developed for univariate signals, mostly of which are developed to remove the transient period in discrete-event simulations [17]. According to Robinson and Davies [18, 19], these methods can be classified into five categories: (1) graphical methods, such as time-series inspection [20], CUSUM plots method [21], exponentially weighted moving average method (EWMA) [22], and statistical process control method [19]; (2) heuristic approaches (e.g. the marginal standard error rules [23, 24]) which offer some simple and straightforward rules to Proceedings of the ASME 2018 13th International Manufacturing Science and Engineering Conference MSEC2018 June 18-22, 2018, College Station, TX, USA

An Efficient Method for Online Identification of Steady State for Multivariate System