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## Model-based Systems Engineering

### Statistical Identification of Systems Engineering Models

“System identification” is a method to build mathematical models from system inputs and outputs. However, it is not just a classic technology. Rather, as the complexity of systems increases, new technologies must be applied. The aim of this project is to develop the new methods and technologies needed to construct abstract models of very complex systems with linkages to those physical systems, even if the number of required parameters is huge and each complex system cannot yet be fully described in any mathematical form.

The increasing complexity of systems does more than increase of the level of detail required in the descriptive models. The complexity also means that the entire integrated system has to be considered, which may include such components as a physics-based fluid model, a mechanical-engineering-based model, and a chemical-reaction-based model. In the past, each of these models might have been studied and analyzed separately. In such multi-physics systems[1], a first-principles-based method starting from the laws of physics and chemistry is an important modeling method. Unfortunately, strict descriptions for the behavior of systems can become too complex and intractable, and sometimes it is difficult to express the mathematical forms needed for designing a specific controller. Therefore, the behaviors of a system (or a part of a system) may be better described by mathematical models that represent the statistical characteristics of the input and output data. At the same time, in multi-physics systems the identified parametric model[2] should be linked to the the physical and chemical laws from which the model is derived.

The OMG (Object Management Group) has defined SysML, a description language for systems modeling. SysML is a modeling language that visualizes the structure, requirements, and constraints of entire systems and of the relationships between them. Our project is developing modeling methodologies for system identification within the SysML framework.

In general, the target of system identification (a physical entity called a “plant”) has many complex subsystems and layered structures. For example, assume that a complex system consisting of subsystems is a target to be controlled. When selecting a control strategy[3], conventional control engineers tend to heuristically choose complex control strategies such as nonlinear control strategies and their combinations without having clear reasons for their choices. However, we want to reconsider why a control strategy is suitable for the system and how the strategy is related to the nonlinearity or combinatorial nature, and to clearly reflect these reasons into the systems model. Describing the results of system identification in the SysML framework can clarify the meaning of the corresponding requirements and physical laws to confirm that an appropriate control strategy was used. As a result, even if the plant is complex and the number of identified parameters is huge, we can derive a clearer and better control strategy. Also, since SysML can describe layered structures, we can derive a better control strategy at the upper level when we combine multiple optimized controllers from subsystems into an entire system.

- [1] Systems that involve multiple physical models of different physical areas, or multiple simultaneous physical phenomena.
- [2] A model that represents a system structure using a finite number of parameters.
- [3] Control strategy is a technical term in control engineering, which refers to how to make the decision on the choice of the control method or means, or a choice of evaluation formula for a quantitative assessment. An example of control strategy could be (1) a simple method that reduces value when it exceeds a threshold, (2) PID (Proportional Integral Derivative) control that decides the control value based on the proportion, differentiation, or integration of the difference between the system output and the reference value, or (3) LQR (Linear Quadratic Regulator) that minimizes the sum of the squares of the differences between the system outputs and the reference values.

### Technologies

For such modeling, we are studying these two technologies:

#### Model-based System Identification Cloud (MbSIC)

Conventional system identification methods have focused on the relatively small numbers of parameters. But as system complexity increases, there are cases in which we must work with enormous amounts of data and many parameters. To address this problem, we are devising technologies for parameter estimation by parallel processing with a nonlinear least squares method that uses the large computation resources of cloud computing.In some plant models, the approximate models are used due to the difficulty of precisely describing the physical laws. Conventionally, parameter estimation for such approximate models assumes white Gaussian noise for the error components, but there are cases where precise observation shows that the error components are biased in their spectral components. To obtain accurate parameters, we must cancel the bias by parametric modeling of the structure of the errors. These kinds of observed data for model calibration tend to have weak signals, and thus larger noise compared to the power of the data (in other words, low SNR (signal-to-noise ratio)). In contrast, the conventional system identification methods may also lack robustness with low SNR signals. To address these problems, we are working on new technologies such as nonlinear system identification methods using nonlinear filtering to extract the necessary information even with a low SNR.

#### Controller Design and Verification

In the SysML diagrams, since there are multiple types of models that are not in mathematical forms, a simulation is performed iteratively while preserving the physical meaning. This allows us to search for the most effective parameter sets. However, this means we need a smooth linkage between the system parameters and the control algorithm in SysML, so we are developing tools for this purpose.In addition to using the SysML model to describe the entire system, we are creating tools for analyzing and verifying the detailed behavior of systems. Using these tools, we can easily verify the behavior of any system since the internal states of the systems are revealed by animations of sequential diagrams and state machine diagrams. To verify whether or not the identified model is working appropriately to satisfy the system requirements, we can combine other signal flow models and inputs as needed, so we can simulate the behavior of the full system using the Plant Model Integration developed within our project. Using these controller design tools, we can also explore new control strategies.