Parameterisation of a product and an activity

1 Introduction

This document explains the usage of the EACM modules to support the internal parameterisation of a product or activity - i.e. the identification of points or features within a product or states within an activity. This parameterisation can then be used to describe variations of properties with respect to position within a product or stage within an activity.

The modules covered by this document are:

product feature space;
activity and state space; and
product activity and state space parameterisation.

2 A product design

A designer creates a design for a product that specifies the following information:

the product is a beam;
the product has a rectangular cross section;
the product has a length of 10 metres, depth of 4 metres and breadth of 2 metres;
the design is called '10 metre 4´2 rectangular beam'.

Using the terminology of the ARM for this part of ISO 10303, the designer creates a Specific_product_specification.

The Specific_product_specification '10 metre 4´2 rectangular beam' is a class that has individual beams as members. Each individual beam that is 10 metres long and that has a 4 metres by 2 metres rectangular cross section is a member of this class, or (to put it another way) complies with the design.

The ARM instance corresponding to this product design is as follows:

#001 = SPECIFIC_PRODUCT_SPECIFICATION ();

NOTE - The entity Specific_product_specification is the principal point of intersection with the STEP product structure backbone. There are may facts to record about the product design which are not within the scope of this discussion, including:

the identification of the design;

the classification of the design as a beam with a rectangular cross section;

the possession of the length, breadth and depth properties;

the relationship with previous designs.

3 A set of features within a product design

An analysis of the 10 metre beam can consider the set of cross sections within it. This set of cross sections is a Design_surface_space.

Each cross section is a surface of matter more or less normal to the reference axis of the beam. These surfaces of matter change position and shape as the beam deforms. It is usually convenient to choose the surfaces of matter so that they are flat and normal to the reference axis of the beam in an unloaded reference state.

There are an infinite number of cross sections in the set. Each cross section in the set is identified by a real number in the range [0, 1].

The ARM instances that record:

the existence of the one dimensional space of cross sections;
its relationship to the design as a whole; and
the way in which a cross section within the set is identified,

are as follows:

#002 = DESIGN_SURFACE_SPACE (1);
#003 = FEATURE_SPACE_FOR_PRODUCT_DESIGN (#001, #002);
#004 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION (#005, #002);
#005 = MATHS_SPACE ('the set of reals between 0 and 1');

NOTE - The entity Maths_space is the point of intersection with the Mathematical representation schema. The way in which the nature of the Maths_space is made computer interpretable, is not within the scope of this discussion.

4 An individual feature within a product design

The mid section of the 10 metre beam is a Design_surface.

The ARM instances that record:

the existence of the cross section;
its relationship to the set of cross sections within the beam; and
the identification of the cross section by the number 0.5,

are as follows:

#006 = DESIGN_SURFACE ();
#007 = MEMBERSHIP_OF_FEATURE_SPACE (#002, #006);
#008 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION_ELEMENT (#009, #006);
#009 = MATHS_VALUE ('the real 0.5');
#010 = ELEMENT_OF_PARAMETERISATION (#004, #008);

NOTE - There can be alternative identification schemes for the cross sections. Identifications by the ranges [0, 1] and [-0.5, 0.5] and [-1, 1] are all possible. Also the numbering of the cross sections can start from either end. The entity Element_of_mapping indicates which scheme is used.

NOTE - The entity Maths_value is a point of intersection with the Mathematical representation schema. The way in which the nature of the Maths_value is made computer interpretable, is not within the scope of this discussion. A simple value will be a direct use of the REAL type in an AIM instantiation, rather that an entity.

5 An activity design

An analyst creates the definition or 'design' of an activity that specifies the following information:

the activity is called 'slow loading of 10 metre beam 3 metres from one end';
the activity is performed by the 10 metre beam;
the 10 metre beam is simply supported throughout;
the 10 metre beam is initially unloaded and unstressed;
a point load is applied 3 metres from one end, and slowly increased until it is 10 kN.

Using the terminology of the ARM for this part of ISO 10303, the designer creates an Activity.

The Activity 'slow loading of 10 metre beam 3 metres from one end' is a class that has individual activities as members. Each individual activity that slowly applies a point load 3 metres from the end of a 10 metre beam with a 4 metres by 2 metres rectangular cross section, is a member of this class, or (to put it another way) complies with the design.

The ARM instances that record:

the existence of the activity design; and
its relationship to the product design,

are as follows:

#011 = ACTIVITY ();
#012 = ACTIVITY_ASPECT_OF_PRODUCT (#011, #001);

NOTE - The entity Activity is another point of intersection with the STEP product structure backbone. There are may facts to record about the activity design which are not within the scope of this discussion, including:

the identification of the activity design;

the classification of the activity design as a slow loading process;

the possession of the simply supported boundary conditions throughout the activity design;

the possession of an applied point load that increases during the activity design;

the relationship with previous activity designs.

6 A set of states within an activity design

An analysis of the beam loading activity can consider the set of states that exist during the loading process. This set of states is a State_space.

There are an infinite number of states in the set. Each state in the set is identified by a real number in the range [0, 1].

The ARM instances that record:

the existence of the one dimensional space of states;
its relationship to the activity design as a whole; and
the way in which a state within the set is identified,

are as follows:

#013 = STATE_SPACE (1);
#014 = ACTIVITY_OR_STATE_SPACE_FOR_ACTIVITY (#013, #011);
#015 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION (#005, #013);

NOTE - The same Maths_space is used to identify cross sections and states. There is only one set of reals, but many uses of it.

7 An individual state within a state space

The final loaded state of the 10 metre beam is a State.

The ARM instances that record:

the existence of the final loaded state;
its relationship to the set of states within the activity design; and
the identification of the state by the number 1.0,

are as follows:

#016 = STATE ();
#017 = MEMBERSHIP_OF_STATE_SPACE (#013, #016);
#018 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION_ELEMENT (#019, #016);
#019 = MATHS_VALUE ('the real 1.0');
#020 = ELEMENT_OF_PARAMETERISATION (#015, #018);

NOTE - The entity Maths_value is a point of intersection with the Mathematical representation schema. The way in which the nature of the Maths_value is made computer interpretable, is not within the scope of this discussion. A simple value will be a direct use of the REAL type in an AIM instantiation, rather that an entity.

8 A set of states for features within an activity design

An analysis of the beam loading activity can consider the set of states that exist during the loading process for the set of cross sections of the beam. This set of states for features is a Physical_topology_space.

It can be regarded as the 'product' (i.e. '´') of the space of cross sections for the beam and the space of states for the loading process.

There are an infinite number of states for features in the set. Each state for a feature in the set is identified by a pair of real numbers, where the first identifies the feature and the second the state.

The ARM instances that record:

the existence of the two dimensional space of states for features;
its relationship to the space of states and to the space of features; and
the way in which a state for a feature within the set is identified,

are as follows:

#021 = PHYSICAL_TOPOLOGY_SPACE (2);
#022 = PHYSICAL_SPACE_DESIGN_FEATURE_COMPONENT (#002, #021);
#023 = PHYSICAL_SPACE_ACTIVITY_OR_STATE_COMPONENT (#013, #021);
#024 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION (#025, #021);
#025 = MATHS_SPACE ('the set of real pairs with each component in [0, 1]');
#026 = DERIVATION_OF_PARAMETERISATION (#024, (#004, #015));

NOTE - This parameterisation of the set of states for cross sections can be used to describe any property of a cross section that varies with position along the beam, and with stage in the loading process.

The description can have the form of a function as follows:

the domain is the set of real pairs with each component in [0, 1], which is a parameterisation of the set of states for cross sections; and

the range is the numeric space that identifies the property.

9 An individual state for a cross section

The mid section of the 10 metre beam in the final loaded state is a State for a Design_surface.

This State is a member of the set of states for cross sections.

The ARM instances that record:

the existence of the final loaded state for the mid section;
its relationship to the mid-section;
its relationship to the set of states for cross sections; and
the identification of the state by the pair (0.5, 1.0),

are as follows:

#027 = STATE ();
#029 = STATE_ASPECT_OF_PRODUCT (#027, #006);
#029 = CLASSIFICATION (#021, #027);
#030 = PHYSICAL_TOPOLOGY_SPACE_PARAMETERISATION_ELEMENT (#031, #027);
#031 = MATHS_VALUE ('the real pair (0.5, 1.0)');
#032 = ELEMENT_OF_PARAMETERISATION (#024, #030);

NOTE - Any properties calculated or measured for the mid section of the beam in the loaded state that be associated with this state for a feature.