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733
734 | class Bridge(Structure):
"""Legacy dict-based generator for arch, suspension, and truss bridges built from mirrored half-spans.
Unlike the CEM-based generators, force densities are prescribed
directly per element type rather than solved via form-finding.
"""
param_dtypes = {
"span": float,
"n_cables": int,
"n_bays": int,
"midspan_height": float,
"deck_width": float,
"twist": float,
"cable_distance": float,
"deck_rise": float,
"deck_force": float,
"cable_force": float,
"brace_force": float,
"inter_cable_force": float,
}
def __init__(self, **kwargs):
"""
Args:
span (float): Approximate span of the bridge.
n_cables (int): Number of cables (or arches). Should be equal to 1 or 2.
n_bays (int): Number of bays on each half of the bridge span.
midspan_height (float): Vertical distance between the cables (or arches) and the deck at midspan.
deck_width (float): Horizontal width of the deck.
twist (float): Twist angle (in degrees) of the cables(s) at midspan.
cable_distance (float): Horizontal distance between the cables when n_cables = 2.
deck_rise (float): Rise of the deck as a fraction of the span.
deck_force (float): Force in the longitudinal deck elements at midspan.
cable_force (float): Force in the longitudinal cable elements at midspan.
brace_force (float): Force in the diagonal brace elements.
inter_cable_force (float): Force in the elements connecting the cables when n_cable = 2.
"""
# Check validity of input arguments
for param, value in kwargs.items():
if param in self.param_dtypes and not np.issubdtype(
type(value), self.param_dtypes[param]
):
raise TypeError(
f"Expected type {self.param_dtypes[param]} for parameter '{param}', got {type(value)}"
)
elif param not in self.param_dtypes:
raise ValueError(f"Unexpected parameter: '{param}'")
self.kwargs = kwargs
# Sample random (missing) input parameters
span = self.kwargs["span"] if "span" in self.kwargs else None
self.params = self.sample_input(span=span)
self._set_dict_attr(self.params)
# Derived attributes
self.bay_size = 0.5 * self.span / self.n_bays
line_load = 0.5
point_load = line_load * self.span / (2 * (2 * self.n_bays + 1))
self.load = np.array((0.0, 0.0, -point_load))
# Initialize bridge
self.nodes = {}
self.edges = {}
self.init_procedure()
def init_procedure(self):
"""Procedure run at object initialization"""
self.formfind()
self.mirror_structure()
self.title_color = "black" if self._verify_equilibrium(verbose=False) else "red"
@staticmethod
def sample_input(span=None):
"""Sample random input parameters"""
cable_force_sign = np.random.choice([-1, 1])
braced = np.random.choice([True, False], p=[0.3, 0.7])
twisted = np.random.choice([True, False], p=[0.3, 0.7])
span = np.random.uniform(40, 100) if span is None else span
params = {
"span": span,
"n_cables": np.random.choice([1, 2]),
"n_bays": np.random.randint(
math.ceil(0.5 * span / 7), math.floor(0.5 * span / 3) + 1
), # max, min bay_size = 7, 3
"midspan_height": (
span * cable_force_sign * np.random.uniform(-0.3, -0.1)
if braced
else span * cable_force_sign * np.random.uniform(-0.2, 0.05)
),
"deck_width": np.random.uniform(2.0, 5.0),
"twist": np.random.uniform(5.0, 20.0) if twisted and not braced else 0.0,
"cable_distance": np.random.uniform(3.0, 20.0),
"deck_rise": 0.0
if braced
else np.random.choice([0.0, np.random.uniform(0.02, 0.1)], p=[0.7, 0.3]),
"deck_force": np.random.uniform(-1.5, -3.0),
"cable_force": cable_force_sign * np.random.uniform(3.0, 15.0),
"brace_force": 1.0 if braced else 0.0,
"inter_cable_force": 0.0
if braced
else np.random.choice([0, np.random.uniform(-1.0, 1.0)]),
}
return params
def formfind(self, threshold=5e-4, update_straight_trail_force=True):
"""Main form-finding algorithm"""
# Initialize first deck nodes
self._set_node(
0,
np.array([0.0, 0.5 * self.deck_width, 0.0]),
0.5 * self.load,
external_force=np.array([-self.deck_force, 0.0, 0.0]),
sem_type="deck",
origin=True,
)
self._set_node(
1,
np.array([0.0, -0.5 * self.deck_width, 0.0]),
0.5 * self.load,
external_force=np.array([-self.deck_force, 0.0, 0.0]),
sem_type="deck",
origin=True,
)
# Initialize first cable nodes
cable_force_vector = np.array([-self.cable_force, 0.0, 0.0])
twist_radians = np.radians(self.twist)
R_z = np.array(
[
[np.cos(twist_radians), -np.sin(twist_radians), 0],
[np.sin(twist_radians), np.cos(twist_radians), 0],
[0, 0, 1],
]
)
cable_force_vector = R_z.dot(cable_force_vector)
if self.n_cables == 1:
self._set_node(
2,
np.array([0.0, 0.0, self.midspan_height]),
np.zeros(3),
external_force=np.copy(cable_force_vector),
sem_type="cable",
origin=True,
)
else:
self._set_node(
2,
np.array([0.0, 0.5 * self.cable_distance, self.midspan_height]),
np.zeros(3),
external_force=np.copy(cable_force_vector),
sem_type="cable",
origin=True,
)
self._set_node(
3,
np.array([0.0, -0.5 * self.cable_distance, self.midspan_height]),
np.zeros(3),
external_force=np.copy(cable_force_vector),
sem_type="cable",
origin=True,
)
for i in range(self.n_bays):
# Set node indices
prev_left_deck_node_idx = i * (2 + self.n_cables)
prev_right_deck_node_idx = prev_left_deck_node_idx + 1
prev_left_cable_node_idx = prev_right_deck_node_idx + 1
next_left_deck_node_idx = prev_left_cable_node_idx + self.n_cables
next_right_deck_node_idx = next_left_deck_node_idx + 1
next_left_cable_node_idx = next_right_deck_node_idx + 1
if self.n_cables == 2:
prev_right_cable_node_idx = prev_left_cable_node_idx + 1
next_right_cable_node_idx = next_left_cable_node_idx + 1
# Determine vertical node offset
z_offset = (2 * i + 1) * self.deck_rise * self.span / self.n_bays**2
# Determine hangar forces
left_hangar_force = self._hangar_force(
prev_left_deck_node_idx, prev_left_cable_node_idx, z_offset=z_offset
)
self._set_edge(
(prev_left_deck_node_idx, prev_left_cable_node_idx),
left_hangar_force,
"deviation",
"hangar",
)
cable_node_idx = (
prev_left_cable_node_idx
if self.n_cables == 1
else prev_right_cable_node_idx
)
right_hangar_force = self._hangar_force(
prev_right_deck_node_idx, cable_node_idx, z_offset=z_offset
)
self._set_edge(
(prev_right_deck_node_idx, cable_node_idx),
right_hangar_force,
"deviation",
"hangar",
)
# Set inter-deck edge
inter_deck_force = self._inter_deck_force(
prev_left_deck_node_idx, prev_right_deck_node_idx
)
self._set_edge(
(prev_left_deck_node_idx, prev_right_deck_node_idx),
inter_deck_force,
"deviation",
"inter-deck",
)
# Determine next deck nodes and edges
next_left_deck_coords, left_deck_force = self._next_node(
prev_left_deck_node_idx, self.bay_size
)
self._set_node(
next_left_deck_node_idx,
next_left_deck_coords,
self.load,
sem_type="deck",
)
self._set_edge(
(prev_left_deck_node_idx, next_left_deck_node_idx),
left_deck_force,
"trail",
"deck",
)
next_right_deck_coords, right_deck_force = self._next_node(
prev_right_deck_node_idx, self.bay_size
)
self._set_node(
next_right_deck_node_idx,
next_right_deck_coords,
self.load,
sem_type="deck",
)
self._set_edge(
(prev_right_deck_node_idx, next_right_deck_node_idx),
right_deck_force,
"trail",
"deck",
)
# Determine brace forces
if self.brace_force != 0.0:
brace_factor = self.brace_force / (-self.n_cables + 3)
left_brace_force = self._brace_force(
prev_left_cable_node_idx,
next_left_deck_node_idx,
factor=brace_factor,
)
right_brace_force = self._brace_force(
cable_node_idx, next_right_deck_node_idx, factor=brace_factor
)
self._set_edge(
(prev_left_cable_node_idx, next_left_deck_node_idx),
left_brace_force,
"deviation",
"brace",
)
self._set_edge(
(cable_node_idx, next_right_deck_node_idx),
right_brace_force,
"deviation",
"brace",
)
# Set inter-cable edges
if self.n_cables == 2 and self.inter_cable_force != 0.0:
self._set_edge(
(prev_left_cable_node_idx, prev_right_cable_node_idx),
self.inter_cable_force,
"deviation",
"inter-cable",
)
# Determine next cable node and edge
next_left_cable_coords, cable_force = self._next_node(
prev_left_cable_node_idx, self.bay_size
)
self._set_node(
next_left_cable_node_idx,
next_left_cable_coords,
np.zeros(3),
sem_type="cable",
)
self._set_edge(
(prev_left_cable_node_idx, next_left_cable_node_idx),
cable_force,
"trail",
"cable",
)
if self.n_cables == 2:
next_right_cable_coords, cable_force = self._next_node(
prev_right_cable_node_idx, self.bay_size
)
self._set_node(
next_right_cable_node_idx,
next_right_cable_coords,
np.zeros(3),
sem_type="cable",
)
self._set_edge(
(prev_right_cable_node_idx, next_right_cable_node_idx),
cable_force,
"trail",
"cable",
)
# Add reaction force as external force
support_nodes = [
next_left_deck_node_idx,
next_right_deck_node_idx,
next_left_cable_node_idx,
]
if self.n_cables == 2:
support_nodes.append(next_right_cable_node_idx)
for node_idx in support_nodes:
resultant = self._resultant(node_idx)
self.nodes[node_idx]["external_force"] = -resultant
self.nodes[node_idx]["support"] = True
# Update straight trail forces for horizontal reaction forces to be zero
if update_straight_trail_force:
# Update deck forces and corresponding external forces
deck_straight = (
1
- self._force_direction(
prev_left_deck_node_idx, next_left_deck_node_idx
)[0]
< threshold
)
if (
deck_straight
and abs(self.nodes[next_left_deck_node_idx]["external_force"][0])
> threshold
):
deck_force_update = (
-self.nodes[next_left_deck_node_idx]["external_force"][0] - 1e-4
)
self.params["deck_force"] += deck_force_update
self.nodes[next_left_deck_node_idx]["external_force"][0] += (
deck_force_update
)
self.nodes[0]["external_force"][0] -= deck_force_update
self.nodes[next_right_deck_node_idx]["external_force"][0] += (
deck_force_update
)
self.nodes[1]["external_force"][0] -= deck_force_update
for edge, edge_info in self.edges.items():
if edge_info["semantic_type"] == "deck":
self.edges[edge]["force"] += deck_force_update
# Update cable forces and corresponding external forces
cable_straight = (
1
- self._force_direction(
prev_left_cable_node_idx, next_left_cable_node_idx
)[0]
< threshold
)
if (
cable_straight
and abs(self.nodes[next_left_cable_node_idx]["external_force"][0])
> threshold
):
cable_force_update = (
-self.nodes[next_left_cable_node_idx]["external_force"][0] - 1e-5
)
self.params["cable_force"] += cable_force_update
self.nodes[next_left_cable_node_idx]["external_force"][0] += (
cable_force_update
)
self.nodes[2]["external_force"][0] -= cable_force_update
if self.n_cables == 2:
self.nodes[next_right_cable_node_idx]["external_force"][0] += (
cable_force_update
)
self.nodes[3]["external_force"][0] -= cable_force_update
for edge, edge_info in self.edges.items():
if edge_info["semantic_type"] == "cable":
self.edges[edge]["force"] += cable_force_update
self._set_dict_attr(self.params)
def _hangar_force(self, deck_node_idx, cable_node_idx, z_offset=0):
"""Determine hangar force that ensures a next deck node with specified vertical offset"""
direction = self._force_direction(deck_node_idx, cable_node_idx)
resultant = self._resultant(deck_node_idx)
force = -(resultant[2] + z_offset / self.bay_size * resultant[0]) / direction[2]
return force
def _inter_deck_force(self, left_deck_node_idx, right_deck_node_idx):
"""Determine inter-deck force that ensures a constant-width deck"""
left_resultant = self._resultant(left_deck_node_idx)
right_resultant = self._resultant(right_deck_node_idx)
x_1, y_1, _ = left_resultant
x_2, y_2, _ = right_resultant
force = (x_2 * y_1 - x_1 * y_2) / (x_1 + x_2)
return force
def _brace_force(self, cable_node_idx, deck_node_idx, factor):
"""Determine brace force that ensures a flat cable"""
direction = self._force_direction(cable_node_idx, deck_node_idx)
resultant = self._resultant(cable_node_idx, ignore_sem_type="cable")
force = -resultant[2] / direction[2]
return force * factor
def _next_node(self, prev_node_idx, bay_size):
"""Determine the next node coordinates and corresponding connecting edge force"""
coords = self.nodes[prev_node_idx]["coordinates"]
force_vector = self._resultant(prev_node_idx)
sign = -np.sign(force_vector[0])
force = sign * np.linalg.norm(force_vector)
factor = bay_size / abs(force_vector[0])
new_coords = -sign * factor * force_vector + coords
return new_coords, force
def mirror_structure(self):
"""Mirror structure across the yz plane"""
mirrored_nodes = {}
nodes_to_skip = (
{0: 1, 1: 0, 2: 2} if self.n_cables == 1 else {0: 1, 1: 0, 2: 3, 3: 2}
)
new_idx_offset = max(self.nodes.keys()) + 1 - len(nodes_to_skip)
# Mirror nodes and adjust load for nodes not mirrored
for node_idx, node_info in self.nodes.items():
if node_idx in nodes_to_skip:
if "external_force" in node_info:
del node_info["external_force"]
node_info["load"] = np.array(node_info["load"]) * 2
continue
if "external_force" in node_info:
mirrored_external_force = np.array(node_info["external_force"])
mirrored_external_force[0] = -mirrored_external_force[0]
mirrored_external_force[1] = -mirrored_external_force[1]
mirrored_coords = np.array(node_info["coordinates"])
mirrored_coords[0] = -mirrored_coords[0]
mirrored_coords[1] = -mirrored_coords[1]
new_idx = node_idx + new_idx_offset
mirrored_nodes[new_idx] = {**node_info, "coordinates": mirrored_coords}
if "external_force" in node_info:
mirrored_nodes[new_idx]["external_force"] = mirrored_external_force
self.nodes.update(mirrored_nodes)
# Mirror edges and adjust force for edges not mirrored
mirrored_edges = {}
for (start_idx, end_idx), edge_info in self.edges.items():
mirrored_start_idx = (
nodes_to_skip[start_idx]
if start_idx in nodes_to_skip
else start_idx + new_idx_offset
)
mirrored_end_idx = (
nodes_to_skip[end_idx]
if end_idx in nodes_to_skip
else end_idx + new_idx_offset
)
if not (start_idx in nodes_to_skip and end_idx in nodes_to_skip):
mirrored_edges[(mirrored_start_idx, mirrored_end_idx)] = edge_info
else:
edge_info["force"] *= 2
self.edges.update(mirrored_edges)
def create_feature_dict(self):
"""Derive a dict of descriptive features (typology, dimensions, load path, etc.) from this bridge.
Returns:
dict: the sampled parameters plus derived features such as
``typology``, ``curved_deck``, ``alignment``, ``height``,
``load_path``, and member length statistics.
"""
self.array_output()
coords = self.array_dict["coordinates_node"]
# support_node_indices = set(self.array_dict['support_node_indices'][0])
# origin_node_indices = set(self.array_dict['origin_node_indices'][0])
# cable_node_indices = set(self.array_dict['cable_node_indices'][0])
# arch_mid_height = coords[list(cable_node_indices.intersection(origin_node_indices))[0]][2]
# arch_base_height = coords[list(cable_node_indices.intersection(support_node_indices))[0]][2]
# arch_rise = arch_mid_height - arch_base_height
bbox_length, bbox_width, bbox_height = coords.max(axis=0) - coords.min(axis=0)
feature_dict = self.params.copy()
# Populate feature dictionary
if self.brace_force > 1e-4:
feature_dict["typology"] = "truss bridge"
feature_dict["number_of_cables"] = 0
feature_dict["number_of_arches"] = 0
elif self.cable_force < 0:
feature_dict["typology"] = "arch bridge"
feature_dict["number_of_arches"] = self.n_cables
feature_dict["number_of_cables"] = 0
elif self.cable_force > 0:
feature_dict["number_of_cables"] = self.n_cables
feature_dict["number_of_arches"] = 0
if self.midspan_height > 0:
feature_dict["typology"] = "suspension bridge"
if "typology" not in feature_dict:
feature_dict["typology"] = "hybrid"
if self.deck_rise > 1e-4:
feature_dict["curved_deck"] = True
else:
feature_dict["curved_deck"] = False
if self.twist > 1e-4:
feature_dict["alignment"] = "twisted"
else:
feature_dict["alignment"] = "straight"
feature_dict["height"] = bbox_height
feature_dict["load_path"] = self.load_path()
feature_dict["average_member_length"] = self.average_member_length()
feature_dict["minimum_member_length"] = self.minimum_member_length()
feature_dict["maximum_member_length"] = self.maximum_member_length()
# feature_dict['passed_filter'] = self.passed_filter()
return feature_dict
def create_request_dict(self):
"""Return [create_feature_dict][torch_structure.generators.bridge.Bridge.create_feature_dict]'s output, stripped of the underlying sampling parameters."""
request_dict = self.create_feature_dict()
# del request_dict['passed_filter']
del request_dict["n_cables"]
del request_dict["twist"]
del request_dict["brace_force"]
del request_dict["inter_cable_force"]
del request_dict["cable_force"]
del request_dict["deck_force"]
del request_dict["midspan_height"]
del request_dict["deck_rise"]
del request_dict["cable_distance"]
return request_dict
# def passed_filter(self):
# if bridge_filter.maximum_load_path(self, factor=1.0) and bridge_filter.within_bbox(self) and bridge_filter.deck_smoothness(self) and bridge_filter.maximum_force(self) and self._verify_equilibrium():
# return True
# else:
# return False
def array_output(self):
"""Create edge and node attribute numpy array outputs"""
self.array_dict = {}
# Save edge attributes
self.array_dict["edge_index"] = np.array(list(self.edges.keys()))
self.array_dict["trail_edge"] = np.array(
[edge["cem_type"] == "trail" for edge in self.edges.values()]
)
self.array_dict["deviation_edge"] = np.array(
[edge["cem_type"] == "deviation" for edge in self.edges.values()]
)
self.array_dict["deck_edge"] = np.array(
[edge["semantic_type"] == "deck" for edge in self.edges.values()]
)
self.array_dict["cable_edge"] = np.array(
[edge["semantic_type"] == "cable" for edge in self.edges.values()]
)
self.array_dict["hangar_edge"] = np.array(
[edge["semantic_type"] == "hangar" for edge in self.edges.values()]
)
self.array_dict["force_edge"] = np.array(
[edge["force"] for edge in self.edges.values()]
)
self.array_dict["length_edge"] = np.array(
[edge["length"] for edge in self.edges.values()]
)
# Save node attributes
self.array_dict["coordinates_node"] = np.array(
[node["coordinates"] for node in self.nodes.values()]
)
self.array_dict["load_node"] = np.array(
[node["load"] for node in self.nodes.values()]
)
self.array_dict["support_node"] = np.array(
[node["support"] for node in self.nodes.values()]
)
self.array_dict["support_node_indices"] = np.where(
self.array_dict["support_node"]
)
self.array_dict["origin_node"] = np.array(
[node["origin"] for node in self.nodes.values()]
)
self.array_dict["origin_node_indices"] = np.where(
self.array_dict["origin_node"]
)
self.array_dict["deck_node"] = np.array(
[node["semantic_type"] == "deck" for node in self.nodes.values()]
)
self.array_dict["deck_node_indices"] = np.where(self.array_dict["deck_node"])
self.array_dict["cable_node"] = np.array(
[node["semantic_type"] == "cable" for node in self.nodes.values()]
)
self.array_dict["cable_node_indices"] = np.where(self.array_dict["cable_node"])
return self.array_dict
def pyg_data(self):
"""Convert this bridge to a `torch_geometric.data.Data` graph.
Returns:
tuple[torch_geometric.data.Data, dict]: the graph, with node
features ``[x, y, z, x_load, y_load, z_load, support]`` and
edge feature ``force_density``, and a metadata dict describing
each feature column.
"""
self.array_output()
meta_data = {}
# Node features
coordinates_node = torch.tensor(
self.array_dict["coordinates_node"], dtype=torch.float64
)
load_node = torch.tensor(self.array_dict["load_node"], dtype=torch.float64)
support_node = torch.tensor(
self.array_dict["support_node"], dtype=torch.float64
).unsqueeze(1)
meta_data["node_features"] = {
0: {"description": "x_coordinate", "type": "numerical"},
1: {"description": "y_xoordinate", "type": "numerical"},
2: {"description": "z_xoordinate", "type": "numerical"},
3: {"description": "x_load", "type": "numerical"},
4: {"description": "y_load", "type": "numerical"},
5: {"description": "z_load", "type": "numerical"},
6: {
"description": "support condition (0 = free, 1 = pinned)",
"type": "categorical",
},
}
node_features = torch.cat([coordinates_node, load_node, support_node], dim=1)
# Edge features
force_edge = torch.tensor(
self.array_dict["force_edge"], dtype=torch.float64
).unsqueeze(1)
length_edge = torch.tensor(
self.array_dict["length_edge"], dtype=torch.float64
).unsqueeze(1)
force_density_edge = force_edge / length_edge
meta_data["edge_features"] = {
# 0: {'description': 'force', 'type': 'numerical'},
0: {"description": "force_density", "type": "numerical"}
}
edge_features = torch.cat([force_density_edge], dim=1)
# Edge index
edge_index = (
torch.tensor(self.array_dict["edge_index"], dtype=torch.long)
.t()
.contiguous()
)
undirected_edge_index, undirected_edge_features = (
torch_geometric.utils.to_undirected(edge_index, edge_attr=edge_features)
)
# Create PyTorch Geometric data object
pyg_data = Data(
x=node_features,
edge_index=undirected_edge_index,
edge_attr=undirected_edge_features,
)
return pyg_data, meta_data
def plot(self, ax=None, plot_threshold=1e-4, plot_deck=True, path=None):
"""Plot bridge structure in 3D"""
show = False
if ax is None:
fig = plt.figure(figsize=(20, 20))
ax = fig.add_subplot(111, projection="3d")
show = True
for edge in self.edges:
force = self.edges[edge]["force"]
if abs(force) < plot_threshold:
continue
color = self.red_color if force >= 0 else self.blue_color
x_coords = (
self.nodes[edge[0]]["coordinates"][0],
self.nodes[edge[1]]["coordinates"][0],
)
y_coords = (
self.nodes[edge[0]]["coordinates"][1],
self.nodes[edge[1]]["coordinates"][1],
)
z_coords = (
self.nodes[edge[0]]["coordinates"][2],
self.nodes[edge[1]]["coordinates"][2],
)
ax.plot(x_coords, y_coords, z_coords, color=color)
if plot_deck:
self.array_output()
coords = self.array_dict["coordinates_node"][self.array_dict["deck_node"]]
coords = np.concatenate(
(
coords[0 : (self.n_bays + 1) * 2 : 2],
coords[(self.n_bays + 1) * 2 - 1 : 0 : -2],
coords[(self.n_bays + 2) * 2 :: 2],
coords[-1 : (self.n_bays + 1) * 2 + 1 : -2],
)
)
ax.add_collection3d(Poly3DCollection([coords], color="grey", alpha=0.4))
ax.set_proj_type("ortho")
ax.axis("equal")
ax.set_axis_off()
load_path = self.load_path()
ax.set_title(
f"Span = {self.span:.1f} | LP = {load_path:.1f}", color=self.title_color
)
if path:
plt.savefig(f"{path}.png", bbox_inches="tight")
elif show:
plt.show()
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