1. Develop a decision-making (DM) CBM method applicable to intelligent machines whose dynamics may be approximated by a parametric nonlinear model and are subject to nonstationary excitation.
2. Simulate the DM/CBM of a simplified robot actuator as a proof of concept.
3. Develop a software framework for the implementation of DM/CBM in a high-bandwidth real-time test environment.

Decision-Making CBM Concept We are currently developing DM/CBM to overcome the problems that Vasquez’s work brought to light. DM/CBM makes use of actuator performance envelops, which translate an actuator’s current condition to its global capabilities. The residuals between an actuator’s healthy performance envelope, its required performance envelope, and the envelope associated with its current condition are converted to DM criteria that are intuitively understandable (e.g. % health margin), even to an operator with no engineering experience. Here are the basic steps: Step 1) Performance Criteria: The quality of an actuator’s output must be defined in a measurable way. These output metrics are called performance criteria. Although a rotary actuator is a torque producing device, other qualities like efficiency and torque ripple are also important and should be used as appropriate for a given task. Generally, the same performance criteria that were used in determining which actuator to spec for a job will be the same criteria used by the DM/CBM system to determine if the actuator is able to continue doing its job. Step 2) System Model: The performance criteria for a nominal (healthy) actuator must be mapped over its entire range of operation. This is done empirically, through careful metrology and thorough testing. Then a parameterized physics-based model (ODE) of the actuator is derived, which relates actuator states and inputs to performance criteria outputs. The model must capture enough of the underlying nonlinear physical phenomena to accurately reproduce the empirically generated performance envelopes. Least squares smoothing techniques are useful for calibrating the model to the performance envelope data [10].

Fig 2. DM/CBM Flow Chart

Step 3) System Identification: In order to monitor the condition of the actuator and to decide when an incipient fault is compromising it, real-time updated actuator performance envelopes are generated. For this purpose, a system identification algorithm, called an Extended Kalman Filter, is implemented [10]. The Extended Kalman Filter continuously updates the model, which can then be used to generate the updated performance envelopes, referred to as the assessed condition.

Step 4) Required Performance Condition: A foundational tenant of decision making systems is that they must incorporate knowledge of the task for which the system is used [3]. In the case of actuators, the task envelope is called the required performance condition (RPC). This assumes that the engineer who initially selected the actuator, knew what its purpose was, and included a margin of safety in his/her calculations. The RPC defines the condition for which an actuator could still adequately complete its task, but with zero margin of safety.

Step 5) Decision Criteria: Convert these global residuals to intuitive decision criteria based on the actuator’s required performance condition (RPC). These decision criteria are:

• % Health Margin is a measure of an actuator’s instantaneous condition. It is a means of summarizing the progress of the actuator’s assessed condition as it degrades from healthy toward the PRC. % Health Margin can come in many forms like minimum health, average health, and RMS health. For example, Fig 5 shows how minimum health is calculated from the ratio of the absolute and relative residuals. The red triangle denotes the value for the minimum health.
• % Certainty is a measure of the statistical certainty of the % health margin. It is used to avoid false alarms. Currently, % certainty is calculated using Kline-McClintock uncertainty analysis, though methods utilizing higher-order statistics would be more effective.
• Remaining Useful Life is an estimate of the time left before % health margin reaches zero. By monitoring the progress of % health over time, an estimate of the time remaining before % health reaches zero may be calculated.

Step 6) The Fault Decision: After all of the effort expended to obtain decision criteria, their use is both logical and simple. The decision criteria essentially convert a multidimensional residual problem into a scalar threshold decision. If the % health is lower than permitted or the time to failure is less than required and the % certainty is high enough, then a fault is declared. At this point, the fault is verifiably non-trivial; it is not just a false alarm that will be shrugged off as software malfunction because the operator specifies, through the RPC and the permissible values of the decision criteria, what amount of performance degradation is allowable for the given task. As shown in Figure 2, the fault decision can be used to trigger a fault diagnosis process if desired.

How DM/CBM Resolves the Difficulties with Standard CBM

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In order to show a preliminary proof of concept of the DM/CBM algorithms, a simulation was conducted (Refer to the figure The Way DM/CBM Works below). The simulated actuator is a three phase direct-drive permanent magnet synchronous motor. In order to provide realistic excitation, load torque and (command) velocity time series were taken from a 7-DOF serial manipulator (ALPHA arm) simulation, which was conducted by Rios and Kapoor [11]. Three types of incipient multiplicative faults were injected into the actuator model: increased bearing friction, permanent magnet degradation, and increased phase winding resistance. An Extended Kalman Filter (EKF) served as the system identification algorithm. It estimates both the states of the actuator model and parameters associated with the three faults. The EKF passes the estimated parameters to the performance envelope generator. The performance envelope generator uses the estimated parameters to generate a steady state torque vs. speed vs. efficiency performance envelope, which represents the assessed condition of the actuator. For simplicity, a vector required performance envelope was arbitrarily chosen and archived. It is a scaled version of the nominal condition: 85% in the direction of torque and speed, 80% in the efficiency direction. The upper bounds of the health margin criteria were calculated using a 95% level of certainty. Also, the remaining useful life of the actuator was calculated based a windowed linear regression of the relative min health margin. The final decision logic was this: if the health margin was less than two percent or the remaining useful life was less than 5 seconds (time had to be scaled for the purposes of simulation), then the actuator should be replaced; if not, continue operation.

The simulations demonstrate that DM/CBM can detect individual and/or simultaneous incipient multiplicative faults of different types, with different incipient rates. DM/CBM was shown to operate effectively using the natural excitation of a common robot task. Also, the simulation results showed that DM/CBM performed favorably when compared with the statistical change detection of model parameter estimates, which is a common model based monitoring method.

Selected DM/CBM Simulation Results:

1. Animation: Pan View of the Simulated Performance Envelope.

2. Animation: Health Margin Degradation Due to Increased Bearing Friction.

3. Animation: Health Margin Degradation Due to a Magnet Aging.

4. Animation: Health Margin Degradation Due to Increased Winding Resistance.

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