Sensor Placement User Manual

1Getting Started

1.1What Sensor Placement Does

Sensor Placement answers two questions before a gauge is bonded: how many strain rosettes does this test need, and where do they go?

It works by simulating the whole test. A linear-elastic plane finite element model of your part is solved for a family of loads the article may see. Every candidate sensor layout is then scored by running the same peridynamic strain recovery that Field Recovery will run after the test, and comparing the recovered field with the finite element field. The layout that reconstructs the field best wins.

Because the estimator being optimised is the estimator you will actually use, the error reported here is the error you should expect from the real test — not a proxy such as condition number or mode coverage.

1.2When to Use It

• Planning instrumentation for a coupon, component or full-scale test article.
• Justifying a channel count to a customer or a certification authority.
• Siting a permanent structural-health-monitoring array, which must serve loads that are not yet known.
• Checking an instrumentation plan someone else drew, by scoring it against an optimised layout of the same size.

1.3The Main Window

PDRecovery holds two workspaces that share one model. The workspace bar at the top of the window switches between them:

Below it, the step bar shows the six steps of the Sensor Placement workspace. Ctrl+1 to Ctrl+6 jump between them. The first three steps — Domain, Discretization, Boundary & Material — are shared with Field Recovery and edit the same project data, so work done in one workspace is immediately available in the other.

The window is split between the canvas, which draws the part, the peridynamic points, the candidate positions and the sensors, and the step panel on the right, which holds the settings and results of the active step. Every panel ends with navigation buttons to the previous and next step.

1.4Projects, Units and Undo

A project is a single .pdrx file. It stores the geometry, the peridynamic points, the boundary conditions, the nominal material, the placement settings and every optimised layout, so re-opening a project restores the whole study without re-running it.

The project carries a length unit, and every length field in the panels shows it as a suffix. Choose it once, in the Domain step, and stay with it; a DXF import reads the drawing's own unit and scales it to the project unit for you.

Undo and redo are unlimited (Ctrl+Z, Ctrl+Y) and have a history panel. Geometry edits, discretization, boundary roles and placement settings are all undoable.

2Workflow — Step by Step

The six steps run in order. Steps 1 to 3 build the model, steps 4 to 6 design the layout.

2.1Step 1 — Domain

Build the two-dimensional domain from shapes. Every shape is either a part, which adds material, or a cut-out, which removes it; the domain is the union of the parts minus the union of the cut-outs. Any shape can be suppressed without deleting it.

Drawing shapes

Clicking without dragging opens a numeric form at that point instead. Add Shape by Coordinates (Ins) opens the same form as a panel, and keeps it open so you can enter a series of shapes.

The Select tool (S) moves shapes, resizes them with the corner handles (Ctrl resizes symmetrically, Shift keeps the aspect ratio), and rotates them with the round handle (Shift steps by 15°). A selected polygon shows a square handle at each vertex to move it, a round handle at the middle of each side to insert a vertex, and a right-click menu to delete the vertex under the cursor. Sides that would cross are refused. Any shape can be converted to a polygon, with curves becoming 64 segments.

Grid snapping (G) and object snapping (O) to centres, vertices, edge midpoints and quadrants are both available; hold Alt while dragging to suppress them.

Importing geometry

Two import routes avoid drawing altogether.

• DXF drawing (File ▸ Import DXF Drawing…, Ctrl+Shift+I). Lines, arcs, circles, ellipses, splines, polylines with bulges and block references are read from the model space. Open curves are joined end to end within a join tolerance; curves are converted to segments within a chord tolerance, with their inner vertices marked smooth so that an arc remains a single boundary edge; full circles and ellipses stay exact. Closed outlines are nested by containment, so an outline inside an odd number of others becomes a cut-out — a plate outline with holes imports as one part and its holes. The panel lists every outline with its role, type, vertex count, area and layer, previews them on the canvas, reads the drawing unit from $INSUNITS and lets you set the scale to the project unit. The import adds to or replaces the domain as a single undo step.
• CSV import and export of the shape table. Polygons list their vertices in a vertices column as x y; x y; ….

The panel reports the net area, the boundary length, the number of regions and holes, and warns about cut-outs with no effect, disconnected regions and an empty domain.

2.2Step 2 — Discretization

The discretization produces the peridynamic points and their cell areas. In Sensor Placement it does double duty: the points are where the error is measured, and — for the discrete search methods — they are also the candidate sensor positions.

The result panel reports the number of points, the sum of the cell areas against the domain area, the smallest and largest cell, and the nearest-neighbour spacing. Points are drawn coloured by cell area, and hovering over one shows its coordinates and area.

2.3Step 3 — Boundary & Material

This step, shared with Field Recovery, says how the article is held and loaded, and what it is made of.

Edges

The boundary of the domain — outer boundaries and holes alike — is split into edges at corners and wherever it passes from one shape's outline to another's. An L-shaped part has six straight edges; a circular hole is one closed edge; an arc added as a fillet is its own edge. Each edge keeps a stable identity through moves, resizes and rotations of its shape. Select an edge on the canvas or in the edge list and give it a role:

Edges without a role of their own inherit the role of another piece of the same shape side — a notch that splits a side does not lose its role — and otherwise the role of the bounding-box side they lie on. By default the left side is supported and the right side loadable.

Nominal material

Set Young's modulus E, Poisson's ratio ν, and the plane hypothesis (plane stress or plane strain). The material here is nominal: Sensor Placement assumes it, and Field Recovery later identifies the real one from the measurements.

At least one edge must be marked loadable, and at least one supported, before the load model can be solved.

2.4Step 4 — Load Model

The load model says which loads the layout must cope with. A layout optimised for one load case can be poor for another, so the model is deliberately a family rather than a single case.

Each load is a traction on one loadable edge, either normal (along the outward normal, which follows a curved edge) or shear (along the tangent), varying along the edge as a Legendre polynomial. The polynomial degree sets how rich the family is:

Tractions selects which components enter the model: normal and shear, normal only, or shear only. A known uniform tension, as in the published examples, is degree 0, normal only.

Every load is scaled to unit RMS strain, so all count equally in the objective and a single stiff load case cannot dominate the design.

Held-out loads

Alongside the design loads, the tool builds a set of held-out loads — one polynomial degree higher, plus localised patch loads. These are never used to design a layout. They are scored afterwards, and they tell you whether a layout has been over-fitted to the design family or is genuinely good. Watch them whenever the real load is uncertain.

Previewing

Preview Strain Fields solves the finite element model for every load and draws the selected one on the peridynamic points, as the equivalent strain or a single component. Use it as a sanity check: if a preview does not look like the test you are planning, the supports or the loadable edges are wrong, and no amount of optimisation will fix that.

2.5Step 5 — Candidates

Candidates are the positions a sensor may occupy. By default they are the peridynamic points; three constraints narrow them down to positions a technician can actually use.

The panel reports the number of candidate positions, the total number of peridynamic points and the excluded zones with their radius, and the canvas draws them. It warns when there are fewer candidates than the sensor budget of step 6, and when the constraints have left too few candidates to work with at all.

2.6Step 6 — Optimise

This is where the layouts are designed. Layouts are optimised at N = N min, N min + step, …, N max, so the result is not a single layout but a curve of accuracy against cost.

Settings

How a layout is built

1. The first layout, at N min, starts from space-filling positions.
2. Every later layout starts from the optimised layout of the previous N, plus the extra sensors, each added where the current error is largest — chosen from the error hot spots and a few random positions.
3. A swap refinement then moves each sensor in turn to the best of the error hot spots, its neighbouring peridynamic points and a few random positions, keeping the move only if the error falls. Passes repeat until a pass moves nothing, or the pass limit is reached.

Trials are scored on a coarser quadrature of the peridynamic points for speed; the errors reported for the finished layouts use all of them. Progress, the current N and the running error are shown live, and Optimise turns into Stop while the search runs — stopping keeps the layouts finished so far.

Refining a single N

Below the results, Optimise N works on one sensor count at a time. Enter a new N and it is optimised starting from the next smaller optimised layout; enter an N that already has a layout and it receives further refinement passes. Use it to fill a gap in the curve, or to push the one layout you actually intend to build.

2.7Exporting the Sensor Plan

The Sensors box lists the coordinates of the selected layout, and the canvas draws them on the part. Export Sensor Plan… writes a CSV file with the sensor id, x and y, and empty strain columns.

That file is the bridge between the two halves of a test campaign:

1. Export the plan and take it to the laboratory. The coordinates are in the project's length unit, in the project's coordinate frame.
2. Bond the rosettes at those positions and run the test.
3. Fill the measured strains into the empty columns.
4. Switch to the Field Recovery workspace (Ctrl+Alt+R) and import the same file in step 4, Sensors & Data.

3Choosing the Settings

3.1Choosing a Search Method

Five methods are available. The first three keep sensors on peridynamic points; the last two let them take continuous coordinates anywhere in the material.

The continuous methods place sensors off the peridynamic points. That is realistic — a technician does not bond a gauge to a grid node — but it means the exported coordinates will not coincide with points, and the number of Gauss-Newton steps is set in the Advanced box.

3.2Choosing a Polynomial Degree

The degree is the single most consequential choice in the study, because it decides what "good" means.

• If the test applies a load you control and know — a uniform tension in a testing machine — use degree 0 and the matching traction component. The design family is then the real load, and the optimisation has nothing to hedge against.
• If the load introduction is imperfect, or the article is loaded through a fitting, degree 1 or 2 buys robustness cheaply.
• For monitoring, where the service load is genuinely unknown, use a higher degree and then judge the layouts by their held-out error rather than their design error.

A higher degree makes the problem harder, so the design error rises. That is not a worse layout; it is a wider question being answered.

3.3Sensor Noise and Target Error

Sensor noise is given as a percentage of the largest strain of each component. It adds a term to the objective proportional to the squared recovery weights, which penalises layouts whose reconstruction amplifies noise — the ill-conditioned clusters an error-driven search would otherwise be tempted by. Set it to the noise floor of your instrumentation relative to the strain level you expect. The reported Amplification tells you how much the layout multiplies it.

Target error drives the recommendation. Set it to the accuracy the test must deliver, and the tool recommends the smallest N whose worst component error meets it. Leave it at 0 and the recommendation is the knee of the curve — the point beyond which extra gauges stop paying for themselves.

3.4Advanced Settings

4Reading the Results

4.1The Error Curve

The plot at the top of the results shows the error of the optimised layout against the number of sensors, with the recommended N marked and the total optimisation time reported. Click any point on the curve, or pick a value from the N box, to load that layout: the canvas draws it, the sensor table lists it, and the statistics below update.

Read the curve for its shape, not only for its recommendation. A steep stretch means each extra gauge still buys accuracy; a flat stretch means the layout has saturated what the geometry and the load family allow, and more channels are wasted money.

4.2The Error Numbers

For the selected layout the panel reports:

A component that nearly vanishes in a load — shear in a pure-tension case, for instance — is measured against a small floor rather than against its own tiny maximum, so it cannot dominate the objective through division by almost nothing.

4.3Held-Out Loads and the Baseline

These two numbers are the quality control of the study, and they are worth more attention than the design error.

• Held-out error close to the design error. The layout generalises; it is good for loads outside the model.
• Held-out error much worse than the design error. The layout is specialised to the design family. That is exactly right when you know the load and wrong when you do not — raise the polynomial degree and optimise again.
• Optimised error barely better than space-filling. Either the field is nearly uniform, so position hardly matters, or the constraints in step 5 have left the search no freedom. Check the candidate count.

4.4Optimisation History

The small plot below the statistics shows the error after every accepted move while that layout was optimised. A curve that has flattened means the search converged; a curve still falling at the end means more passes, or a higher effort setting, would still help.

5Worked Example

The validation case is a 4 m × 4 m plate with a central hole of radius 0.5 m, clamped on the left edge and loaded in uniform tension on the right, discretized at Δx = 0.04 m. The design load is the known tension alone: degree 0, normal only. Layouts were optimised for 16, 28, 40, 50, 60 and 72 sensors, and then scored against a finite element reference field with the same peridynamic recovery (n_neighbors = 16) used for every other layout.

Two conclusions carry over to real tests. At the same gauge count, optimisation was worth roughly a factor of five against the published layout. And accuracy better than a carefully hand-made 68-sensor layout was reached with 50 optimised sensors — a 26 % reduction in channels for a better result.

6Tips and Troubleshooting

6.1How Long It Takes

Optimisation time grows with the number of peridynamic points, the number of loads in the model, the number of values of N, and the effort setting. The dominant cost is scoring trial layouts, which is memory-bound, so extra worker processes help only up to a point.

• To explore quickly, use POD + pivoted QR, a coarse grid and a wide step. Seconds.
• For the study you will report, use the exchange search on the grid you intend to use for Field Recovery. Minutes.
• Refine only the layout you will build, with Optimise N and a thorough search.

The search can be stopped at any time; the layouts finished so far are kept, and are saved in the project.

6.2Common Problems

7Reference

7.1Mouse and Keyboard

7.2Glossary