Servomotor Dataset: Modeling Health in Mechanisms with Typically Intermittent Operation

Servomotors are used in a variety of industrial applications where precise movements are of critical importance. Degradation mechanisms in servomotors have been mostly studied and modeled for systems with long duration steady state modes. However, some specialized applications require health estimation from very short duration intermittent operations, which require different analysis techniques. With such applications in mind, a simulated dataset for servomotor health modeling and prediction is described and made available for public use. The application scenario is motivated by a fine motion control rod drive (FMCRD) mechanism used for intermittent, and typically infrequent, fine motion (insertion or withdrawal) adjustment of control rods in some nuclear reactor designs. Though the drives do not run continuously, servomotor and associated linear motion mechanisms do show wear and damage during its operational lifetime. Specifically, in FMCRD such degradations may be caused by internal as well as external damage to the system. While the causes of such damage can be diverse, in simulation we model the impact of cumulative damage as an external opposing load which resists the movement of the motor shaft. Such scenarios represent effects of rod-binding and debris in the fuel channels. The dataset includes measurements such as motor currents and rotor speed which would be part of the instrumentation in a typical deployments of rotating machinery. These observable measurements can be used to predict the health state of the servomotor. Also presented are baseline results on health state estimation, formulated as classification and regression problems, which can be used by the larger PHM community for performance comparisons. This dataset is hosted at the PHM Society Data repository [https://data.phmsociety.org/servomotor_dataset/].


INTRODUCTION
Servomotors are utilized in a variety of industries for their closed-loop feedback systems that provide high-precision control and accuracy of the rotor's speed and position.The current work is motivated by the use of servomotor drives in some nuclear power plants.In fission reactors, in the context of nuclear power generation, neutron-absorbing control rods are used to modulate the reactivity by precise positioning within the reactor core.While the control rods serve to rapidly shutdown the reactor completely when a safety trigger gets tripped, incremental positioning of the rods, as a part of normal operation, enables optimized power control and core power shaping.The former, also known as a SCRAM, is typically controlled by a hydraulic mechanism.Fine motion control rod drives (FMCRD) are used to operate the control rods for the latter purpose and are driven by electric servomotors.For example, the advanced boiling water reactor (AWBR) by GE Hitachi has a suite of 205 FMCRDs (Chapter 4: Reactor, AWBR: Design Control Document / Tier 2, 2016).More recently, small modular reactors (SMR) have become an important consideration in the energy mix for the flexibility and scalability they afford, among other advantages.The BWRX-300 is a SMR proposed by GE Hitachi Nuclear Energy (GE Hitachi Nuclear Energy, 2023, 2020) which has a similar set of control rods arranged in the reactor core, with each being driven by a dedicated FMCRD.
In both the AWBR and the SMR designs, the FMCRD makes small positional adjustments to the control rods and for a power maneuver.This means that the bulk of the servomotor operation happens in small spurts and the motor does not operate for extended durations.This is in contrast to most rotating machinery that operates on a more continuous basis and sustains wear over steady state operation (e.g., see (Bejaoui, Bruneo, & Xibilia, 2020)).Although the drive operates over short durations, internal as well as external damage can cause impediments to the movement of the rotor shaft, leading to modes of degradation that differ from continually operating servomotors.The prognostics and health management for such an intermittent operational regime is different, and this paper addresses the need for data and algorithms for such applications.Specifically, for machine learning approaches, feature extraction over periods of transient operation requires different preprocessing and signal analysis than features one may extract over continuously operating machinery.Specifically, in this paper we present a simulated dataset for a generic servomotor driven ball-screw mechanism inspired by FMCRD use-case.We first describe the simulator design in Section 2. We discuss the design of experiments and describe the data recorded in Section 3 and in Section 4 discuss observations about the data which also explicates the nature of data over various levels of degradation.Section 5 presents baseline results for health prediction.

SERVOMOTOR SIMULATION
A Mathworks ® Simulink ® Simscape based model is used to build a servomotor simulator with coupled ball-screw mechanical components.The motor system is derived from MathWorks's base three-phase permanent magnet synchronous motor (PMSM) example (The MathWorks, Inc., 2023b, 2023a) and the ball screw system is based on the model used in (Krichen et al., 2020) to simulate a five-axis CNC machine tool.
PMSM are designed to operate at a specific constant speed, in step with the rotating magnetic field.A 220 voltage AC source provides 3-phase sinusoidal voltages to the PMSM.These specific motors use a wound rotor, in which coils of wire are placed in the rotor slots.These coils are excited by an external DC source, slip rings and brushes that are used to supply current to the rotor.The Simulink model diagram is shown in Fig. 1 where the 3-phase motor system (red block) feeds rotor speed and torque data to simulate a force that drives the actuator system (green block).This model demonstrates the implementation for nominal operation, without faults or degradation.
Figure 2 is a simplified schematic representation of the control loop, adapted from Figure 1 in (Fullilove, Santos, Saxena, & Coble, 2022).The degradation mechanism is simulated using a "RESISTIVE LOAD" block which is connected to the load being driven by the actuator.This is apparent when we compare the "green components", i.e., the actuator block in Fig. 1 with the drive mechanism in Fig. 2. The resistive load represents the force acting against the ball screw.Increasing this load mimics the effect of causes of FMCRD degradation such as friction, debris and rod binding.
At a given instant, a demanded position drives the ball screw via the servomotor.A Matlab wrapper interfaces with the Simulink model to enable setting a desired control rod movement/displacement profile.The desired position is compared to the current position measurement of the encoder and the calculated difference is converted by the PID controller to an input speed that corrects and achieves the desired position.Not shown in Fig. 2, but included within the Simulink model, are 2 PI controllers that ramp rotor speed to its desired value.Finally, the 3-phase motor currents are converted to an orthogonal reference frame (direct and quadrature) using the Parke and Clarke transform.Implementing these two transforms in a consecutive manner simplifies computations by converting AC current and voltage waveform into DC signals.
Finally, the output measurements of the model are the stator phase currents, rotor speed, electromagnetic torque, and Qand D-axis phase currents.An external braking system is also used to apply a force to the motor shaft once the desired position is obtained, locking the control rod in place.While the PID controller in its nominal operation is tuned to be a critically damped system, adding the resistive load block changes the control profile.We also add band-limited measurement noise into the feedback loop which further moves the output response to be under-damped under certain realizations of noise and resistive load.Thus the simulator is not an idealized notion of servo control, but indeed incorporates real-world operational conditions.

DATASET DESCRIPTION
In previous work, (Fullilove et al., 2022) have described methods for fault detection, with different fault modes added to the Simulink model described shown in Fig. 1.For this work, the simulator is exercised for generating representative data in the presence of resistive load that acts against the servomotor ball screw mechanism.This section describes the design of experiments and the resulting dataset.
Data are simulated as depicted in Fig. 3.We consider 4 categories of load values denoted as C {c = 0, 1, 2, 3}.These map one-to-one with 4 levels of degradation {'LN', 'LO', 'MED', 'HI'} which denote the labels likenew, low, medium and high, respectively.The load is a latent unobservable variable, but its effects may be manifested in observable signals from the Simulink model.The loads are a sampled from a mixture of Gaussians with distinct modes corresponding to each category c.Consequently, each measurement from the simulation maps to a degradation level (DL ∈ {'LN', 'LO', 'MED', 'HI'}) and a degradation value, DV ∈ R + .Each DV is normally distributed with mean µ DL and standard deviation σ DL .We assume that as part of existing inspection protocols, subject matter experts, SMEs, have a way of determining DV and DL.For this dataset, DV is not upper-bounded, though a user may use suitable monotone functional transforms so that, e.g., DV ∈ [0, 1).(Fullilove et al., 2022).
Table 1 lists the values of µ DL , σ DL .As evident by the histogram in Fig. 4, there is an overlap of DV between adjacent degradation levels.This also mimics the ambiguity in assessments by SMEs about what may constitute a medium vs. high level of degradation.
In exercising the simulator, we also input a randomly generated sequence of demanded rod positions (equivalently rod displacements); every such sequence is called a run.A rod displacement is referred to as a transition in that the rod transitions from a previous position to a new demanded position.For each FMCRD degradation category, we generate 200 distinct runs, which consists of an initial rod position and a sequence of 5 transitions (demanded displacements) of the control rod over a period of 6 seconds.This is simply an accelerated mechanism to simulate an ensemble of typical displacements of the control rod.A run of transitions, however, may not necessarily be a typical sequence of what is com-   The data are hosted at the PHM Society Data Repository (Subramanian et al., 2023).
The panel of 6 plots at the bottom of Fig. 5 shows the degra- In fact, two closely spaced degradation values, as sampled from the degradation profile in the top panel of Fig. 5, may be separated by a considerable gap in time.It is also important to note that since runs are simulated as IID samples from an underlying distribution, 2 successive runs may be considered to be realizations from an ensemble of similar control rods and drives.This also mimics what is typical: deployment as bank of a control rods and drives.One may apply various damage propagation models such as those considered by (Saxena, Goebel, Simon, & Eklund, 2008) or (Liang et al., 2014) to simulate time-to-failure data, but this is not within the scope of our approach.

HEALTH MODELING AND PREDICTION
In this section, the dataset is used for modeling and predicting the health state of the FMCRD.Two setups are considered: • Classification, where ylabel is used as a target; • Regression, where real valued DV is the target Simple features are used to setup baseline results.Recall that in the context of the problems being considered, only segments of time-series data while the rod is in motion (transient data) is useful.We first segment the transient portion of the data -this is easily extracted by allowing for a tolerance of convergence between the demanded and actual rod position, as well as using a persistent return-to-zero logic in signals such as rotor speed or torque.For each transition, a transient segment is split into 3 equal time intervals and median values for rotor speed and quadrature current are computed over each interval.Including del_pos, we get a 7-dimensional feature vector.
To solve the classification problem, we train a random forest classifier, the results for which are presented in Fig. 7 and Table 3.Using the same feature set, we also train with DV as the response variable using a random forest and a support vector regressor (SVR) with a radial basis kernel.The scatter  plots of predicted vs. actual ( Y vs. ) is presented in Fig. 8a and Fig. 8b.While the SVR model achieves a lower mean absolute error (MAE) compared to the random forest regressor, the forest of decision rules is able learn a decision region that excludes DV < 0. This likely has implications for generalizability when the model encounters data in regimes where it has not seen training data.

CONCLUSION
We described a simulated dataset for fine motion motion control rod drives, which are operated intermittently and age as a function of transient usage.The datasets are designed for machine learning approaches to model and degradation: we have generated training and testing sets, with measurement data that is typically available during deployment, and data labels which may be treated as SME evaluations.This paper also discusses baseline results which can be used for performance comparisons.We encourage users to consider ways in which the data can be used for health prediction, prognostics and decision aiding by using better algorithms or imposing different constraints.As part of current and future work we are also evaluating the suitability of releasing the Simulink model and simulation scripts for public use.

Figure 5 .Figure 6 .Figure 7 .
Figure5.Runs and transitions for different loads.Note that all transitions corresponding to given run have the same degradation value; however, two distinct runs will have distinct DV s.

Figure 8 .
Figure 8. Scatter plot of Y vs. Y for health state estimation as a regression problem using (a) random forest regressor and (b) a support vector regressor.

Table 1 .
Simulation parameters for load categories.
DL types).The data are stored as CSV files.Table2provides a description the various columns in the dataset.
ylabel ∈ {"LN", "LO", "MED", "HI"} dation values, and demanded and actual displacements, for pairs of consecutive runs sampled from different low, medium and high degradation levels.As one can observe, each run consists of transitions corresponding to positive or negative displacements of the control rod.In the dataset, runs are indexed by run_index, and transitions are indexed by the column labeled transitions.While the run_index values in each subplot are consecutive, this does not imply that it is a function of usage or life since the runs are random draws from the underlying sampling distributions.Temporal information indicating life or usage history is not explicitly modeled.