1、_ SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising there
2、from, is the sole responsibility of the user.” SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions. Copyright 2006 SAE International All rights reserved. No part of this publication m
3、ay be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. TO PLACE A DOCUMENT ORDER: Tel: 877-606-7323 (inside USA and Canada) Tel: 724-776-4970 (outside USA)
4、 Fax: 724-776-0790 Email: CustomerServicesae.org SAE WEB ADDRESS: http:/www.sae.org J2748 ISSUED OCT2006 SURFACE VEHICLE RECOMMENDED PRACTICE Issued 2006-10 VHDL-AMS Statistical Analysis Packages RATIONALE Not applicable. FOREWORD The SAE J2748 is based on the IEEE Std. 1076.1-1999, the VHDL-AMS lan
5、guage definition. It provides support for modeling of statistical information that is relevant to automotive systems. INTRODUCTION This document specifies the interface and the behavior of the VHDL-AMS packages for use in modeling statistical behavior. These packages are useful in defining the stati
6、stical variation of parameters of electrical, electronic, and mechatronic components and sub-systems. These can then be used with simulation tools to analyze the performance and reliability of systems composed of these components and sub-systems. SAE J2748 Issued OCT2006 - 2 - TABLE OF CONTENTS 1. S
7、COPE 3 1.1 Purpose. 3 2. REFERENCES 3 2.1 Applicable Publications . 3 2.1.1 IEEE Publications 3 2.2 Related Publications . 3 2.2.1 SAE Publications. 3 3. PACKAGE DEFINITIONS. 4 3.1 STATISTICS . 4 3.1.1 Types 4 3.1.2 Attributes . 5 3.1.3 Auxiliary Functions 6 3.1.4 Regular Distribution Functions 9 3.
8、1.5 Standard Distribution Functions 35 3.2 STATISTICS_CONTROL 43 3.2.1 Types 43 3.2.2 Functions. 44 4. USING THE STATISTICAL PACKAGES 45 4.1 Using Statistical Functions in VHDL-AMS Models . 45 4.1.1 Library and Package Names. 45 4.1.2 Specifying a distribution for a constant within a model. 45 4.1.3
9、 Assigning a distribution to a generic in a generic map . 46 4.1.4 Creating a model that includes generic constants for the distribution 47 4.1.5 Correlation. 47 4.2 Simulation Control. 48 4.2.1 Switching Between Nominal and Statistical Analysis . 48 4.2.2 Seed Management 49 4.2.3 Performing a Stati
10、stical Analysis on a Portion of the Design 49 4.2.4 Extending a Monte Carlo Experiment . 49 4.3 Defining a New Statistical Distribution 49 4.3.1 Naming Conventions. 49 4.3.2 Standard Distribution Functions 50 4.3.3 Attributes . 50 4.3.4 Specific Requirements/Rules 50 4.4 Example 51 5. PACKAGE RATION
11、ALE . 52 5.1 Package Architecture 52 5.1.1 Package STATISTICS_CONTROL 52 5.1.2 Package STATISTICS . 52 5.1.3 Design Library. 52 5.2 Statistical Distribution Functions. 52 5.2.1 Regular Distribution Functions 53 5.2.2 Standard Distribution Functions 56 6. NOTES 56 6.1 Key Words. 56 SAE J2748 Issued O
12、CT2006 - 3 - 1. SCOPE This document specifies the interface and the behavior of the VHDL-AMS packages for use in modeling statistical behavior. These packages are useful in defining the statistical variation of parameters of electrical, electronic, and mechatronic components and sub-systems. These c
13、an then be used with simulation tools to analyze the performance and reliability of systems composed of these components and sub-systems. Providing a standard definition of the package interfaces and their behavior is intended to facilitate the exchange of models between component and system manufac
14、turers and the use of different CAE simulation tools. The SAE statistical package supports the statistical modeling of design parameters subject to tolerances for designs described using the VHDL or VHDL-AMS languages. The performance of a design that uses this package to model parameter tolerances
15、may be analyzed by a Monte Carlo simulation, which consists of multiple simulation runs of the design, each run with a different set of parameter values according to their statistical distributions. The Monte Carlo simulation will yield an estimate of the behavior of the design subject to the parame
16、ter tolerances. Additionally, the package may be used to perform an Extreme Value Analysis of a design, that is, an analysis that computes the worst case behavior of the design. The SAE statistical package does not support other statistical modeling needs, for example the modeling of statistical var
17、iations of the arrival of events in a queue, or any other situation where a value exhibits a statistical behavior during a single simulation. 1.1 Purpose The VHDL-AMS Statistical Analysis Packages define a common set of standards in defining and using statstical variation of parameters on models wri
18、tten in VHDL-AMS for automotive electrical, electronic, and mechatronic components and sub-systems. The definition supports the use of predefined and user-defined distributions. 2. REFERENCES 2.1 Applicable Publications The following publications form a part of this specification to the extent speci
19、fied herein. Unless otherwise specified, the latest issue of SAE publications shall apply. 2.1.1 IEEE Publications Available from ANSI, 25 West 43rd Street, New York, NY 10036-8002, Tel: 212-642-4900, www.ansi.org or http:/standards.ieee.org. IEEE Std 1076.1-1999 IEEE Standard VHDL Analog and Mixed
20、Signal Extensions 2.2 Related Publications The following publications are provided for information purposes only and are not a required part of this document. 2.2.1 SAE Publications Available from SAE, 400 Commonwealth Drive, Warrendale, PA 15096-0001, Tel: 877-606-7323 (inside USA and Canada) or 72
21、4-776-4970 (outside USA), www.sae.org. SAE J2546 Model Specification Process Standard SAE J2748 Issued OCT2006 - 4 - 3. PACKAGE DEFINITIONS There are two packages which are used to define the statistical behavior: STATISTICS_CONTROL and STATISTICS. These packages are located in the library with the
22、logical name VHDL_UTILITY. A reference implementation of these packages can be found on the website at http:/links.sae.org/J2748. 3.1 STATISTICS The STATISTICS package defines the types, attributes, auxiliary functions, regular and standard distributions functions. More information can be found in S
23、ection 5.2 on Statistical Distribution Functions. 3.1.1 Types The following types are defined for use with the package. 3.1.1.1 REAL_XY_PAIR Type REAL_XY_PAIR Declaration type REAL_XY_PAIR is record X: REAL; Y: REAL; end record; Record type holding abscissa and ordinate of a point in 2D Fields Name
24、Type Description X REAL abscissa value Y REAL ordinate value 3.1.1.2 REAL_XY_TABLE Type REAL_XY_TABLE Declaration type REAL_XY_TABLE is array (NATURAL range ) of INTEGER_XY_PAIR; Array type holding a sequence of INTEGER_XY_PAIR 3.1.1.5 STAT_MODE_TYPE Type STAT_MODE_TYPE Declaration subtype STAT_MODE
25、_TYPE is VHDL_UTILITY.STATISTICS_CONTROL.STAT_CONTROL_SUBTYPE; Enumeration type defining the statistical modes supported by the package 3.1.2 Attributes The following attributes are used with the regular distribution functions. Attribute STAT_POSITION_NOMINAL STAT_POSITION_TOLERANCE STAT_POSITION_MI
26、NVALUE STAT_POSITION_MAXVALUE Declaration attribute STAT_POSITION_NOMINAL: INTEGER; attribute STAT_POSITION_TOLERANCE: INTEGER; attribute STAT_POSITION_MINVALUE: INTEGER; attribute STAT_POSITION_MAXVALUE: INTEGER; Position of NOMINAL, TOLERANCE, MINVALUE, MAXVALUE in formals. These attributes are us
27、ed to give semantics to the formal arguments of the regular distribution functions SAE J2748 Issued OCT2006 - 6 - 3.1.3 Auxiliary Functions The following auxiliary functions are used with the package. 3.1.3.1 STAT_MODE Function STAT_MODE Declaration pure function STAT_MODE return STAT_MODE_TYPE; Fun
28、ction returning the current statistical mode Return STAT_MODE_TYPE The current statistical mode (STAT_NOMINAL or STAT_STATISTICAL) SAE J2748 Issued OCT2006 - 7 - 3.1.3.2 NORMALIZE_TABLE There are 2 forms of the NORMALIZE_TABLE functions with different arguments. Function NORMALIZE_TABLE Declaration
29、pure function NORMALIZE_TABLE( TBL: REAL_XY_TABLE; NOMINAL: REAL; TOL: REAL ) return REAL_XY_TABLE; Function to normalize a table defining a probability density function or a cumulative density function Arguments Name Type Description TBL REAL_XY_TABLETable specifying the PDF or CDF. The abscissa va
30、lues must increase monotonically NOMINAL REAL Nominal value. Must be non-zero TOL REAL Tolerance of the value. Must be 0 Return REAL_XY_TABLE A table normalized to use with the PWL_PDF or PWL_CDF functions Example SAE J2748 Issued OCT2006 - 8 - Function NORMALIZE_TABLE Declaration pure function NORM
31、ALIZE_TABLE( TBL: REAL_XY_TABLE; NOMINAL: REAL; MINVALUE: REAL; MAXVALUE: REAL ) return REAL_XY_TABLE; Function to normalize a table defining a probability density function or a cumulative density function Arguments Name Type Description TBL REAL_XY_TABLETable specifying the PDF or CDF. The abscissa
32、 values must increase monotonically NOMINAL REAL Nominal value MINVALUE REAL Minimum value. Must be NOMINAL Return REAL_XY_TABLE A table normalized to use with the PWL_PDF or PWL_CDF functions Example SAE J2748 Issued OCT2006 - 9 - 3.1.4 Regular Distribution Functions Regular distribution functions
33、are statistical distribution functions that are intended to be called in a design to define the value of a design parameter. More information can be found in Section 5.2.1 on Regular Distribution Functions. 3.1.4.1 UNIFORM There are 4 forms of the UNIFORM distribution with different arguments. These
34、 functions also have attributes defining position arguments. Function UNIFORM Declaration impure function UNIFORM( NOMINAL: REAL; TOL: REAL; MODE: STAT_MODE_TYPE := STAT_MODE ) return REAL; Uniform distribution with REAL nominal value and tolerance Arguments Name Type Default Description NOMINAL REA
35、L Nominal value TOL REAL Tolerance of the value. Must be = 0 MODE STAT_MODE_TYPE STAT_MODE Specifies whether the function should return the nominal value or a random value in the range between the minimum and maximum values. The default is determined based on the value of constant STAT_CONTROL in pa
36、ckage STATISTICS_CONTROL Attributes Name Value STAT_POSITION_NOMINAL 1 STAT_POSITION_TOLERANCE 2 Return REAL See argument MODE Example SAE J2748 Issued OCT2006 - 10 - Function UNIFORM Declaration impure function UNIFORM( NOMINAL: TIME; TOL: REAL; MODE: STAT_MODE_TYPE := STAT_MODE ) return TIME; Unif
37、orm distribution with TIME nominal value and tolerance Arguments Name Type Default Description NOMINAL TIME Nominal value TOL REAL Tolerance of the value. Must be = 0 MODE STAT_MODE_TYPE STAT_MODE Specifies whether the function should return the nominal value or a random value in the range between t
38、he minimum and maximum values. The default is determined based on the value of constant STAT_CONTROL in package STATISTICS_CONTROL Attributes Name Value STAT_POSITION_NOMINAL 1 STAT_POSITION_TOLERANCE 2 Return TIME See argument MODE Example SAE J2748 Issued OCT2006 - 11 - Function UNIFORM Declaratio
39、n impure function UNIFORM( NOMINAL: REAL; MINVALUE: REAL; MAXVALUE: REAL; MODE: STAT_MODE_TYPE := STAT_MODE ) return REAL; Uniform distribution with REAL nominal value and bounds Arguments Name Type Default Description NOMINAL REAL Nominal value MINVALUE REAL Minimum value. Must be = NOMINAL MODE ST
40、AT_MODE_TYPE STAT_MODESpecifies whether the function should return the nominal value or a random value in the range between the minimum and maximum values. The default is determined based on the value of constant STAT_CONTROL in package STATISTICS_CONTROL Attributes Name Value STAT_POSITION_NOMINAL
41、1 STAT_POSITION_MINVALUE 2 STAT_POSITION_MAXVALUE 3 Return REAL See argument MODE Example SAE J2748 Issued OCT2006 - 12 - Function UNIFORM Declaration impure function UNIFORM( NOMINAL: TIME; MINVALUE: TIME; MAXVALUE: TIME; MODE: STAT_MODE_TYPE := STAT_MODE ) return TIME; Uniform distribution with TI
42、ME nominal value and bounds Arguments Name Type Default Description NOMINAL TIME Nominal value MINVALUE TIME Minimum value. Must be = NOMINAL MODE STAT_MODE_TYPE STAT_MODE Specifies whether the function should return the nominal value or a random value in the range between the minimum and maximum va
43、lues. The default is determined based on the value of constant STAT_CONTROL in package STATISTICS_CONTROL Attributes Name Value STAT_POSITION_NOMINAL 1 STAT_POSITION_MINVALUE 2 STAT_POSITION_MAXVALUE 3 Return TIME See argument MODE Example SAE J2748 Issued OCT2006 - 13 - 3.1.4.2 NORMAL There are 4 f
44、orms of the NORMAL distribution with different arguments. These functions also have attributes defining position arguments. Function NORMAL Declarationimpure function NORMAL( NOMINAL: REAL; TOL: REAL; TRUNCATE: BOOLEAN := FALSE; ZSCORE: REAL := 3.0; MODE: STAT_MODE_TYPE := STAT_MODE ) return REAL; N
45、ormal distribution with REAL nominal value and tolerance Arguments Name Type Default Description NOMINAL REAL Nominal value TOL REAL Tolerance of the value. Must be = 0 TRUNCATE BOOLEAN FALSE If TRUE, truncate normal distribution at minimum and maximum values. ZSCORE REAL 3.0 Defines how many standa
46、rd deviations are between minimum and nominal value and between nominal and maximum value MODE STAT_MODE_TYPE STAT_MODESpecifies whether the function should return the nominal value or a random value with minimum and maximum values at NOMINAL +- ZSCORE * std.deviation. The default is determined base
47、d on the value of constant STAT_CONTROL in package STATISTICS_CONTROL Attributes Name Value STAT_POSITION_NOMINAL 1 STAT_POSITION_TOLERANCE 2 Return REAL See argument MODE Example SAE J2748 Issued OCT2006 - 14 - Function NORMAL Declaration impure function NORMAL( NOMINAL: TIME; TOL: REAL; TRUNCATE:
48、BOOLEAN := FALSE; ZSCORE: REAL := 3.0; MODE: STAT_MODE_TYPE := STAT_MODE ) return TIME; Normal distribution with TIME nominal value and tolerance Arguments Name Type Default Description NOMINAL TIME Nominal value TOL REAL Tolerance of the value. Must be = 0 TRUNCATE BOOLEAN FALSE If TRUE, truncate n
49、ormal distribution at minimum and maximum values ZSCORE REAL 3.0 Defines how many standard deviations are between minimum and nominal value and between nominal and maximum value. Must be 0. MODE STAT_MODE_TYPE STAT_MODESpecifies whether the function should return the nominal value or a random value with minimum and maximum values at NOMINAL +- ZSCORE * std.deviation. The default is determined based on the value
