Parameterisation of a product and an activity

Property of a product, activity or state

1 Introduction

This document explains use of the EACM modules to record information about the properties of a product, activity or state.

A property can be a property of a whole product, activity or state. Alternatively, a property can be something that varies from position to position within a product and from state to state within an activity.

The modules covered by this document are:

property;
property space;
property distribution; and
possession of property.

2 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';
the use of the 'ABC' manufacturing specification.

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 to specification ABC' is a class that has individual beams as members. Each individual beam that is 10 metres long, that has a 4 metres by 2 metres rectangular cross section, and that is manufactured according to specification ABC, 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:

#101 = 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 of the design to the manufacturing specification;

the relationship with previous designs.

3 A property space

A standardisation body defines the concept of a life time for a bridge beam. This concept includes:

a specification of what happens during the life;
a criterion for determining that a bridge beam has reached the end of its life.

Using the terminology of the ARM for this part of ISO 10303, the standardisation body defines a Property_space.

The Property_space 'lifetime of bridge beam' is a class that has individual properties, such as a 'bridge beam lifetime of 100 years', as members.

The ARM instance that records:

the existence of this property space; and
the fact that this space is one dimensional,

is as follows:

#102 = PROPERTY_SPACE (1, $);

NOTE - The entity Property_space is the point of intersection with a dictionary of property types. There are may facts to record about the property space which are not within the scope of this discussion, including:

the identification of the property space;

a text definition of the property space with references;

the source of the property space definition;

previous versions of the property space.

This information is addressed by ISO 13584, and is accessed from the EACM by the Property dictionary application module.

Some other instances of Property_space are as follows:

strength of bridge beam

This property space is defined by a standardisation body that specifies:

the way in which the beam is loaded to failure;
the state of the beam when the strength is measured (e.g. at what temperature); and
the necessary precision of the measurement.

density

This property space has a fundamental physical definition. A point within a volume of matter at a state possesses a density.

average density

This property space has a fundamental physical definition. A quantity of matter at a state possesses an average density. An average density can be possessed by a curve, surface or volume of matter.

4 A property

The Property 'bridge beam lifetime greater that 100 years' is a class which has individual bridge beams as members. A bridge beam is a member of the class if it has, or is predicted to have, a life time in the range.

NOTE - The distinction between properties that are predicted and those that are actually observed can be made using the Possession of property validity application module.

The ARM instances that record:

the existence of the range of bridge beam lifetimes from 100 years to infinity;
the description of the range by the real interval from 100 to infinity; and
the relationship of the range to the concept of 'lifetime of bridge beam',

are as follows:

#103 = PROPERTY_RANGE ($);
#104 = MATHS_VALUE ('the real interval from 100 to infinity');
#105 = IDENTIFICATION_OF_PROPERTY (#103, #104);
#106 = MEMBERSHIP_OF_PROPERTY_SPACE (#102, #103);

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 supported by the Maths value application module, and is not within the scope of this discussion.

NOTE - The relationship between the identification of the property range by the real interval from 100 to infinity and the concept of 'year' is supported by the Property identification application module, and is not within the scope of this discussion.

5 Possession of a property by a product design

A '10 metre 4´2 rectangular beam to specification ABC' has a 'bridge beam lifetime greater that 100 years'. This statement means that:

each member of the class that is Specific_product_specification '10 metre 4´2 rectangular beam to specification ABC'; is also
a member of the class that is Property 'bridge beam lifetime greater that 100 years'.

NOTE - The specification that 'each' has the property may not be true. It may be that 99% of beams that are members of '10 metre 4´2 rectangular beam to specification ABC' have a lifetime longer than 100 years. Statistical and probabalistic information about the possession of a property is supported by the Possession of property statistics and probability application module.

The ARM instance that records:

each member of the beam design has the property,

are as follows:

#107 = POSSESSION_OF_PROPERTY (#101, #103);

6 Precise and 'loose' possession of property

6.1 Neglecting variation with state

A 'lifetime of bridge beam' property is possessed by a bridge beam throughout out its life, and is not something that changes from time to time. A 'strength of bridge beam' property is possessed by a particular state of a bridge beam.

The definition of a property may specify some information about the environment in which it is measured, but this does not remove the need to be precise about the state of the object that possesses the property. A prediction of the strength of a beam after 50 years implies a prediction of a test on an individual beam that is simultaneously:

in the state 'after 50 years use'; and
in the state specified for the property 'strength of bridge beam'.

The state specified for the property is implicit in the definition of the property, but the state 'after 50 years of use' must be recorded. This give a complete possession of property statement of the form:

each member of the class that is Specific_product_specification '10 metre 4´2 rectangular beam to specification ABC', when in state 'after 50 years of use'; is also
a member of the class that is Property '50 tonne bridge beam strength'.

It would be correct to insist that a 'length of bridge beam' property cannot be possessed by a Specific_product_specification that is a beam, but only by a State. However, in practice engineers make looser statements such as:

each member of the class that is Specific_product_specification '10 metre 4´2 rectangular beam to specification ABC', is also
a member of the class that is Property '50 tonne bridge beam strength' for all parts of its life of current interest.

In order to support such a looser statement, a Possession_of_property is valid between a Specific_product_specification and a Property, even if that property is defined only for a State.

6.2 Neglecting variation with position

An average density of 4000 Kg m^-3 is possessed by the beam as whole for a particular state. As indicated in the preceding paragraphs, a possession of property between:

the Specific_product_specification that is the beam; and
the Property that is the average density of 4000 Kg m^-3, indicates that the beam has the average density for all parts of its life of current interest.

An 'average density' property is possessed by a state of beam as a whole, and so does not vary from point to point within it. A 'density' property is possessed by a state of a point within the beam.

It would be correct to insist that a 'density' property cannot be possessed by a Specific_product_specification that is a beam or by a State of a beam, but only by a State of a point within a beam. However, in practice engineers make looser statements such as:

each point within the beam at 20 degrees Celsius has the density of 4000 Kg m^-3;

This is supported by a Possession_of_property between the State and the density Property.
each point within the beam has a density of 4000 Kg m^-3 for all states of interest.

This is supported by a Possession_of_property between the Specific_product_specification and the density Property.

If the beam is not homogenous (being reinforced concrete, say), then both these statements are untrue. Instead the State or Specific_product_specification must be associated with a density Property_distribution.

NOTE - The concept of 'density' at a point is itself a 'loose' statement at the next level of precision, because matter is not a continuum if your scale is small enough. This discussion is not yet within the scope of the EACM.

7 A property distribution with respect to position

There is a property distribution with respect to position such that the density is:

7000 Kg m^-3 for a point within the reinforcement; and
2500 Kg m^-3 for a point within the concrete.

The Property_distribution 'predicted density variation in 10 metre metre 4´2 rectangular beam to specification ABC' is a class that has individual beams as members. Each individual beam that is a member of the Specific_product_specification '10 metre 4(2 rectangular beam to specification ABC' is predicted to be also a member of the Property_distribution.

An object that is not a '10 metre metre 4´2 rectangular beam to specification ABC' can have the Property_distribution. Consider a beam that was intended to comply with the design, but that is 'off-spec' for some reason. This beam may still have the predicted density.

In order to define the density distribution, it is first necessary to define the set of points within '10 metre metre 4´2 rectangular beam to specification ABC'. The ARM instances that record:

the existence of the set of points;
the fact that the set of points is a view of the beam design,

are as follows:

#108 = DESIGN_POINT_SPACE (3);
#109 = FEATURE_SPACE_FOR_PRODUCT_DESIGN (#108, #101);

The ARM instances that record:

the existence of the density distribution, and the set of points within it;
the correspondence between points within the distribution and the points within the beam design;
the existence of the density space; and
the mapping between each point in the distribution and a density value (i.e. the function from the distribution space to the density space),

are as follows:

#110 = PROPERTY_DISTRIBUTION ($);
#111 = SPACE_FOR_PROPERTY_DISTRIBUTION (#110, #112);
#112 = PROPERTY_DISTRIBUTION_SPACE (3);
#113 = PROPERTY_DISTRIBUTION_FOR_FEATURE_SPACE (#112, #108);
#114 = PROPERTY_SPACE (1, $); -- density
#115 = PROPERTY_DISTRIBUTION_FUNCTION (#112, #114);

The property distribution function can be described by a mathematical function that has:

a domain that is a parameterisation of the points within the beam, such as a 3D mesh; and
a range that is an identification of the density space (i.e. the set of positive reals).

The ARM instances that record:

the description of the property function by the mathematical function; and
the existence of the mathematical function,

are as follows:

#116 = MAPPING_OF_PHYSICAL_FUNCTION (#115, #117);
#117 = MATHS_FUNCTION ('my function over my mesh');

NOTE - The entity Maths_function is a point of intersection with the Mathematical representation schema. The way in which the nature of the Maths_function is made computer interpretable is supported by the Maths function application module, and is not within the scope of this discussion.

NOTE - The relationship between the mapping of the physical function to the mathematical function and:

the parameterisation (or identification) of points within the beam by the mesh; and

the identification of density values with respect to the Kg m^-3 scale,

is supported by the Physical function mapping application module, and is not within the scope of this discussion.

8 Possession of a property variation with position

The ARM instance that records:

the 'loose' statement that the each beam manufactured to the design has the density distribution throughout out its life,

is as follows:

#118 = POSSESSION_OF_PROPERTY (#101, #110);

Alternatively, it is possible to record the precise statement that:

each beam manufacture to the design, has the density distribution in its as supplied state, when unstressed and at 20 degrees Celsius,

by ARM instances as follows:

#119 = STATE (); -- as supplied, unstressed and at 20 degrees Celsius
#120 = STATE_ASPECT_OF_PRODUCT_DESIGN (#119, #101);
#121 = POSSESSION_OF_PROPERTY (#119, #110);

NOTE - There are may facts to record about the state which are not within the scope of this discussion, including:

the identification of the state;

the classification of the state as an 'as supplied' state;

the temperature distribution property possessed by the state;

the stress distribution property possessed by the state;

the relationship of the state to the manufacturing activity;

the relationship with previous specifications or designs of the state.

9 Possession of a property by a state

A designer or analyst creates the definition or 'design' of a state as follows:

it is possessed by a 10 metre 4´2 rectangular beam to specification ABC;
it occurs after fifty years of use.

A designer or analysis can specify or predict properties for this state.

The State that is '10 metre 4´2 rectangular beam to specification ABC after fifty years of use' is a class that has individual reinforced concrete beams after 50 years of use as members.

This State has a Property that is '50 year of use'. The ARM instances that record:

the existence of the state and its relationship to the product design;
the existence of the property, its description by the number 50, and its membership of the 'length of use' property space; and
the possession of the property by the state,

are as follows:

#122 = STATE (); -- after 50 years of use
#123 = STATE_ASPECT_OF_PRODUCT_DESIGN (#122, #101);
#124 = PROPERTY_SPACE (1, $); -- length of use
#125 = POINT_PROPERTY ($);
#126 = MEMBERSHIP_OF_PROPERTY_SPACE (#124,#125);
#127 = IDENTIFICATION_OF_PROPERTY (#125, #128);
#128 = MATHS_VALUE ('the real 50');
#129 = POSSESSION_OF_PROPERTY (#122, #125);

10 Possession of a property by an activity

A designer or analyst creates the definition or 'design' of an activity as follows:

it is possessed by a 10 metre 4´2 rectangular beam to specification ABC;
it consists of 10⁶ cycles of a 10000 Kg uniformly distributed load.

The Activity '10⁶ cycles of 10000Kg UDL on 10 metre beam' is a class that has individual activities carried out on individual beams as members.

The ARM instances that record:

the existence of the activity, and its relationship to the product design;
the existence of the property, its description by the number 10⁶, and its membership of the 'number of cycles' property space; and
the possession of the property by the activity,

are as follows:

#130 = ACTIVITY ();
#131 = ACTIVITY_ASPECT_OF_PRODUCT (#130, #101);
#132 = PROPERTY_SPACE (1, $) -- number of cycles
#133 = POINT_PROPERTY ($);
#134 = MEMBERSHIP_OF_PROPERTY_SPACE (#132,#133);
#135 = IDENTIFICATION_OF_PROPERTY (#133, #136);
#136 = MATHS_VALUE ('the real number 10E6');
#137 = POSSESSION_OF_PROPERTY (#130, #133);

11 A property distribution with respect to state

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.

The ARM instances that record:

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

are as follows:

#138 = ACTIVITY ();
#139 = ACTIVITY_ASPECT_OF_PRODUCT (#138, #101);

The maximum in-span deflection for the beam increases from state to state during the activity. In order to define the distribution of in-span deflection with respect to state, it is first necessary to define the set of states within 'slow loading of 10 metre beam 3 metres from one end'. The ARM instances that record:

the existence of the set of states;
the fact that the set of states is a view of the loading activity,

are as follows:

#140 = STATE_SPACE (1);
#141 = ACTIVITY_OR_STATE_SPACE_FOR_ACTIVITY (#140, #138);

The ARM instances that record:

the existence of the maximum deflection distribution, and the set of states within it;
the correspondence between states within the distribution and the states within the loading activity;
the existence of the maximum deflection space; and
the mapping between each state in the distribution and a maximum deflection value (i.e. the function from the distribution space to the maximum deflection space),

are as follows:

#142 = PROPERTY_DISTRIBUTION ($);
#143 = SPACE_FOR_PROPERTY_DISTRIBUTION (#142, #144);
#144 = PROPERTY_DISTRIBUTION_SPACE (1);
#145 = PROPERTY_DISTRIBUTION_FOR_ACTIVITY_OR_STATE_SPACE (#144, #140);
#146 = PROPERTY_SPACE (1, $);  - maximum deflection
#147 = PROPERTY_DISTRIBUTION_FUNCTION (#144, #146);

The property distribution function can be described by a mathematical function that has:

a domain that is a parameterisation of the states within the loading activity, such as a load factor from 0 to 1; and
a range that is an identification of the maximum deflection space (i.e. the set of reals).

The ARM instances that record:

the description of the property function by the mathematical function; and
the existence of the mathematical function,

are as follows:

#148 = MAPPING_OF_PHYSICAL_FUNCTION (#147, #149);
#149 = MATHS_FUNCTION ('my function over the [0, 1] load factor domain');

NOTE - The relationship between the mapping of the physical function to the mathematical function and:

the parameterisation (or identification) of states within the activity; and

the identification of maximum deflection values with respect to the metre scale,

is supported by the Physical function mapping application module, and is not within the scope of this discussion.

The ARM instance that records:

each loading activity carried out according to the specification gives rise to the variation of maximum deflection with state,

is as follows:

#150 = POSSESSION_OF_PROPERTY (#138, #142);

A property distribution with respect to position and state

12 A property distribution with respect to position and state

During the activity 'slow loading of 10 metre beam 3 metres from one end' there is a stress variation with respect to position within the beam and state within the activity.

The ARM instances that record:

the existence of the stress distribution, and the set of states for points within it;
the correspondence between states within the distribution and the states within the loading activity;
the correspondence between points within the distribution and points within the loading beam;
the existence of the stress space; and
the mapping between each state for a point in the distribution and a stress value (i.e. the function from the distribution space to the stress space),

are as follows:

#151 = PROPERTY_DISTRIBUTION ($);
#152 = SPACE_FOR_PROPERTY_DISTRIBUTION (#151, #153);
#153 = PROPERTY_DISTRIBUTION_SPACE (4); -- complete space
#154 = PROPERTY_DISTRIBUTION_SPACE (3); -- spatial component
#155 = PHYSICAL_SPACE_DESIGN_FEATURE_COMPONENT (#154, #153);
#156 = PROPERTY_DISTRIBUTION_FOR_FEATURE_SPACE (#154, #108);
#157 = PROPERTY_DISTRIBUTION_SPACE (1); -- state component
#158 = PHYSICAL_SPACE_DESIGN_FEATURE_COMPONENT (#157, #153);
#159 = PROPERTY_DISTRIBUTION_FOR_FEATURE_SPACE (#157, #140);
#160 = PROPERTY_SPACE (6, #161);  - stress
#161 = PROPERTY_SPACE_TENSOR_ORDER_AND_SYMMETRY ();  - symmetric second order tensor
#162 = PROPERTY_DISTRIBUTION_FUNCTION (#153, #160);

NOTE - There are standard instances of Property_space_tensor_order_and_symmetry that indicate the tensor order and symmetry for properties within a Property_space. This is a point of intersection with parts 104 and 209 of ISO 10303.

The Property_distribution_space has 4 dimensions - 3 spatial dimensions within the beam, and 1 state dimension within the activity. These two components of the Property_distribution_space are separated. The spatial component is mapped by a Property_distribution_for_feature_space on to the set of points within the beam. The state component is mapped by a Property_distribution_for_feature_space on to the set of states within the activity.

The property distribution function can be described by a mathematical function that has:

a domain that is a Cartesian product of the parameterisation of the points within the beam (perhaps a unit cube or a finite element mesh) and a parameterisation of the states within the loading activity (perhaps a unit interval); and
a range that is an identification of the stress space (perhaps the set of real 6-tuples or the set of symmetric 3´3 matrices).

The ARM instances that record:

the description of the property function by the mathematical function; and
the existence of the mathematical function,

are as follows:

#163 = MAPPING_OF_PHYSICAL_FUNCTION (#162, #164);
#164 = MATHS_FUNCTION ('my function from R4 to R6');

NOTE - The relationship between the mapping of the physical function to the mathematical function and:

the parameterisation (or identification) of points within the beam;
the parameterisation (or identification) of states within the activity; and
the identification of stress values with respect to the MPa scale and using a vector encoding as (s_xx, s_yy, s_zz, s_xy, s_yz, s_zx),

is supported by the Physical function mapping application module, and is not within the scope of this discussion.

NOTE - The definition of mathematical functions between multi-dimensional mathematical spaces is a speciality of the mathematical representation schema.

The ARM instance that records:

each loading activity carried out according to the specification gives rise to the variation of stress with position and state,

is as follows:

#165 = POSSESSION_OF_PROPERTY (#138, #151);