Optimization method to compensate accelerator performance drifts

Accelerator performance often deteriorates with time during a long period of operation due to secular changes in the machine components or the surrounding environment. In many cases, some tuning knobs are effective in compensating the performance drifts and optimization methods can be used to find the ideal machine setting. However, such intervention usually cannot be done without interrupting user operation as the optimization algorithms can substantially impact the machine’s performance. We propose an optimization algorithm, Safe Robust Conjugate Direction Search, which can perform accelerator tuning while keeping the machine performance within a designated safe envelope. The algorithm builds probability models of the objective function using Lipschitz continuity of the function as well as characteristics of the drifts and applies to the selection of trial solutions to ensure the machine operates safely during tuning. The algorithm can run during normal user operation constantly, or periodically, to compensate for the performance drifts. Simulation and online tests have been done to validate the performance of the algorithm.

Figure 1

Snapshot of the safety probability along the viable range at the end of 1D safety exploration. The safety probability curve is calculated with the seven given observations. The order of sampling is indicated by the number on top of each observation. Orange triangles denote the observations, the blue curve shows the calculated safety probability, and the safety region with safety probability threshold $p_{\mathit{s}}=0.99$ is highlighted in green.

Figure 2

Evolution of the safety probability during a safety exploration on the 1D test problem. The red dot denotes the time and position of the corresponding sampled point.

Figure 3

Parabola fitting at the end of exploration. The purple dashed vertical line indicates the peak position found by the fitting, and the purple region around the peak line shows the uncertainty of the peak position, calculated by the covariance matrix of the parabola fitting.

Figure 4

Test function surface evolution with time. The drifting period $p$ is set to 800, and the drifting amplitude ${\sigma }_d$ is 0.2. The noise level ${\sigma }_n$ is 0.01. The red curve is the peak position of the test function that changes with time.

Figure 5

Snapshot of the safety probability along the parameter range at the end of 1D safety exploration. The safety probability curve is calculated based on the Gaussian random walk drift model with the previous observations (orange triangles). The order of sampling is denoted by the number on top of each observation. The blue curve is the calculated safety probability and the green shaded area shows the safety region, with the safety probability threshold $p_{\mathit{s}}=0.9$.

Figure 6

Evolution of the safety probability during a safety exploration on the drifting 1D test problem. The red dot denotes the time and position of the corresponding sampled point. The safety probability is calculated with the Gaussian random walk drift model.

Figure 7

Determination of the hyperparameters for 2D test problem. Left: variation of the objective function over time; right: objective function vs parameter scan in two directions. The initial solution is set to be the middle point in the 2D normalized decision space (0.5,0.5). The estimations of $L_v$ and ${\sigma }_d$ are 4000 and 0.8, respectively, derived from the scan results

Figure 8

Relationship between the normalized safety margin $\widehat{m}$ and $({\widehat{\delta }}_{\tau },{\widehat{\delta }}_T)$ for parameter space dimension $D=2$ (left) and $D=4$ (right). As it can be seen here, given the same ${\widehat{\delta }}_T$, a larger ${\widehat{\delta }}_{\tau }$ requires a larger safety margin in order for RCDS-S to follow the trend of the drift.

Figure 9

RCDS-S for kicker-bump matching in simulation. Top plot: orange dots show the objective drift caused by the modulated kicker strength at the initial solution. Blue dots denote the objective function during optimization by the RCDS algorithm while green dots show the performance of RCDS-S. The red horizontal line shows the safety threshold. Bottom plot: orange curve shows the modulation on K1, and the other two dotted curves visualize the evolution history of the variables tuned by RCDS-S.

Figure 10

RCDS-S on BTS steering optimization. The objective function is the negated injection efficiency. The orange, blue, and red curves show the cases without tuning, tuning with RCDS, or tuning with RCDS-S, respectively.

Figure 11

RCDS-S on the kicker-bump matching experiment on the SPEAR3 storage ring, with a safety threshold of $50\mathrm{\mu }\mathrm{m}$. Top plot: orange dots show the objective drift caused by the modulated kicker strength at the initial solution. Blue dots denote the optimization performance of the RCDS algorithm while green dots show the performance of RCDS-S. The red horizontal line shows the safety threshold. Bottom plot: orange curve shows the modulation on K1, and the other two dotted curves visualize the evolution history of the variables as they were tuned by RCDS-S.

Figure 12

Snapshot of the safety probability along the viable range at the end of 1D safety exploration. The safety probability curve is calculated based on the alternative drift model with the given observations. Orange triangles denote the observations, and the order of sampling is denoted by the number on top of each observation. The blue curve is the calculated safety probability and the green shaded area shows the safety region with the safety probability threshold $p_{\mathit{s}}=0.9$.

Figure 13

Evolution of the safety probability during a safety exploration on the drifting 1D test problem. The red dot denotes the time and position of the corresponding sampled point. The safety probability is calculated with the alternative drift model.