Transfer learning‐based surrogate‐assisted design optimisation of a five‐phase magnet‐shaping PMSM

 Multi-phase permanent-magnet synchronous machines (MPMSMs) with high reliability due to sufficient fault-tolerant capability have considerable potential for transportation electrification applications. Here, an efficient surrogate-assisted design optimisation method is proposed based on analytical model transfer learning for torque characteristic optimisation of a five-phase magnet-shaping PMSM. By employing transfer learning of the source domain analytical model data and the target domain finite element analysis (FEA) data in surrogate model training, the proposed method can achieve both high accuracy and high efficiency from the merits of FEA- and analytical-based optimisations, respectively. The studied machine with five-phases and harmonic injected surface-mounted PMs to enable harmonic injection for torque capability improvement is introduced and the analytical model is built based on the segmented PM and the complex conformal mapping methods. Besides, the optimal Latin hypercube design (LHD) and Taguchi methods are used to form the source and target domain datasets, respectively, so that data features can be efficiently captured over a wide range of optimisation variables. An optimal design is obtained by multi-objective optimisation using the trained surrogate model, which is prototyped and measured to validate the proposed method. </p

Post surgery axon number and G-ratio are different in the two groups.

<p>Unlesioned, normal nerves (A, B) are similar in both genotypes. Five months after root avulsion/re-implantation (C, D), smaller axons are more abundant in control than in mutant regenerating nerves (quantification in E), and the G-ratio (the ratio of the inner to the outer diameter of the myelin sheath) is higher in mutant than control samples (quantified in F). A–D: Plastic semi-thin sections stained with Toluidine Blue. *: <i>P</i><0.05; **: <i>P</i><0.01; comparison at different sized axons with <i>t</i>-test, n = 3 mice in each group.</p

Macrophages are activated followed root avulsion/re-implantation.

<p>In transverse sections at C5–C7, anti-CD11b immunoreactivity is widely distributed in the white and gray matter on the lesion side with a decreasing trend from day 7 to day 21, in both the control (A–C) and the mutant (D–F). At each time-point, CD11b expression is higher in the control than the mutant (G). VH, ventral horn. *, <i>P</i><0.05; **, <i>P</i><0.01; comparison at different time-points with <i>t</i>-test, n = 4 mice in each group.</p

Regeneration estimated by GAP-43 expression in the post surgery spinal cord.

<p>In transverse sections at C6, GAP-43 immunoreactivity (ir) is concentrated in the ventral horn (VH) on the lesion side on days 7, 14 and 21 post surgery, reaching maximal level on day 14, in both the control (A–C) and the mutant (D–F). At each time-point, GAP-43 expression is higher in the control than the mutant (G). *, <i>P</i><0.05; **, <i>P</i><0.01; comparison at different time-points with <i>t</i>-test, n = 4 mice in each group.</p

<i>Celsr3|Emx1</i> mice show poor recovery of elbow flexion after surgery.

<p>A: Positions of forelimbs and corresponding scores in grooming tests (adapted from Bertelli & Mira, 1993). B: Mean scores of grooming tests pre- and post-surgery in both groups. Before surgery, the mean score around 5 was comparable in both genotypes. Control mice initiated a progressive recovery around 21 days, reaching a mean score of 3.11±0.25 after five months. In the mutant group, a few mice showed functional recovery from one month post surgery, but the mean score from day 21 to 5 months was lower than in control mice (<i>t</i>-test, <i>P</i><0.01, n = 12).</p

Spinal motoneurons are more resistant to the avulsion injury in <i>Celsr3|Emx1</i> than control mice.

<p>C5–C7 segments of spinal cords were collected 5 months post surgery for Nissl staining, anti-NeuN and anti-ChAT immunofluorescence. A–F: Transversal sections at C5–C7 in control (A, C, E) and mutant spinal cord (B, D, F), stained with Nissl (A, B), anti-NeuN (C, D) and anti-ChAT (E, F). Differences in neuron numbers between Intact and Lesion sides are evident and quantified in G, using the Intact/Lesion (R/L) ratios as indexes. *, <i>P</i><0.05; **: <i>P</i><0.01, <i>t</i>-test, n = 6 in each group.</p

After surgery, newly innervated NMJs are less abundant, and muscles more atrophic in <i>Celsr3|Emx1</i> than control mice.

<p>A, B: Five months post surgery, left (L, intact side) and right (R, surgery side) biceps brachii were weighted. The R/L wet weight ratio was 97% in control mice versus 80% in mutant mice (**: <i>P</i><0.01, <i>t</i>-test, n = 10 in each group). C–J: Different classes of NMJ in the biceps at 5 months post surgery, stained with anti-NF200 to label regenerating axon (green), and anti-<i>α</i>-BT to label AchR clusters (red). In remodeled NMJs, thin axon terminals innervate some but not all fragmented AchR clusters (arrows in E, I). Neoformed NMJs are characterized by small AchR clusters innervated by thin axons that lack terminal arbors (asterisks in F, J). Quantification in K, 100 NMJs in each group, n = 4 mice; **: <i>P</i><0.01, one-way ANOVA.</p

Remyelination is less prominent in <i>Celsr3|Emx1</i> than control mice after root avulsion/re-implantation.

<p>Longitudinal and transverse sections of musculocutaneuous nerves, prior to, and at different time-points post surgery, stained with anti-MBP. MBP is highly expressed in intact musculocutaneous nerves, with no difference between genotypes (A–D). After surgery, MBP expression decreases and reaches minimal expression after 7 days in the control and 14 days in the mutant, and then increases gradually (E–P). Q: In mutant nerves, MBP density is significantly higher than in control nerves at 7 days but lower after 14 and 21 days. *: <i>P</i><0.05, comparison at different time-points with <i>t</i>-test, n = 4 in each group.</p

Expression of c-Jun, not Parvalbumin, is increased at the early stage of post-surgery.

<p>C5–C7 spinal segments were prepared for anti-c-Jun and Parvalbumin (PV) immunofluorescence 3 days post surgery. The expression of c-Jun was rapidly increased on injured sides in both groups, mostly in the ventral horn (VH) and the dorsal horn (DH) (A, B). The number of c-Jun positive cells was counted in the VH on both sides, and its ratio of the right side to the left side (R/L) was calculated, showing significant lower in the mutant than in the control (C). PV- positive neurons were easily identified in the middle region of the gray matter (D, E), but the R/L ratio of the cell number showed no statistic difference between two genotypes (F). CC, the central canal; **, <i>P</i><0.01; n = 6 animals in each group for c-Jun immunostaining and n = 3 animals in each group for PV immunostaining; comparison by <i>t</i>-test.</p

Expression profile of neurotrophic factors and receptors 7 days post surgery.

<p>Seven days post surgery, injured (R) and intact (L) sides of C5–C7 segments were collected separately for Western blot with anti- TrkB, p75, BDNF, NT-3 and GDNF antibodies in control (Ctrl) and <i>Celsr3|Emx1</i> (Mut) mice, and <i>β</i>-tubulin was used as a control protein (A). The expression level of each protein was normalized to<i>β</i>-tubulin (B). Comparisons were summarized in C. In control mices, the expression of TrkB and BDNF was significantly decreased, but that of p75 was significantly increased, on injured sides (R) compared to intact sides (L). There was not significant difference in expression of neurotrophic factors and receptors between injured and intact sides in mutant mice. On both sides, the expression level of p75 was significantly lower in the mutant than in the control. On injured sides, the expression of TrkB and BDNF was significantly higher in the mutant than in the control although their expression was comparable on intact sides between two groups. “↓”, lower or decreased expression; “↑”, higher or increased expression; “_”, no significant difference; *, <i>P</i><0.05; **, <i>P</i><0.01; Ctrl-L, left side of control mice; Ctrl-R, right side of control mice; Mut-L, left side of mutant mice; Mut-R, right side of mutant mice. Six animals were used in each group and <i>t</i>-test was used for comparisons.</p