Appendix 1 TABLE 1-1. EXAMPLE OF GROUPED DISCRETE CODES DECIPHER LOGIC Word Slot Subframe Discrete Status Discrete Codes 7 6 5 4 3 2 1 A/P Mode Throttle “OFF” 1 1 0 0 0 0 0 A/P Mode Throttle “RETARD” 1 1 0 0 0 0 1 A/P Mode Throttle “CLAMP” 1 1 0 0 0 1 0 A/P Mode Throttle “SPD/MCH,ALPHA” 1 1 0 0 0 1 1 A/P Mode Throttle “SPD/MCH,FLAP” 1 1 0 0 1 0 0 A/P Mode Throttle “SPD/MCH,SLAT” 1 1 0 0 1 0 1 A/P Mode Throttle “SPEED” 1 1 0 0 1 1 0 A/P Mode Throttle “EPR LIMIT” 1 1 0 0 1 1 1 A/P Mode Throttle “SPD/EPR LIMIT” 0 1 0 0 0
9. VALIDATION OF EU CORRELATION.
a. Correlation Coefficient. Calculate the correlation coefficient between the raw data and the derived data. Table 1-2 may be used to aid this calculation. The following method may be used to calculate the correlation coefficient for a parameter that is linearly converted.
( ) ()[] ()[]() 2/12222 yyNxxN yxyxN1 Σ−Σ××Σ−Σ× Σ×Σ−×Σ×= where, r = correlation coefficient N = number of data points x = raw data (EU) y = derived value (EU) Σ indicates the sum of the values that follow (e.g., Σx equals the sum of all x values)
Appendix 1 TABLE 1-2. CORRELATION TABLE DECIMAL COUNTS TO EU Parameter No. Parameter Conversion Method □ Linear □ Polynomial □ Unique 0A Unique Equation Reference:
1A 2A 3A 4A 5A Data Point No. Raw Data (EU) 10CNTS Derived Value (EU) 1 2 3 4 5 6 7 8 9 10
Appendix 1
b. Calculate the Correlation Coefficient. Table 1-3 demonstrates the steps in solving for the correlation coefficient.
TABLE 1-3. CORRELATION COEFFICIENT CALCULATION Parameter No. ___ Parameter Name _____________________________ Mnemonic Code _____________ Parameter Word Location ___________________ Subframe _______________ Superframe Cycle ___________________ Assigned Bits (1 through 12) __________________ Range (EU) ______________________ Sign Convention ______________________________ Correlation Coefficient _________ Data Pt No.
x Raw Data (EU) y Derived Value (EU) 2x 2y y×x 1 2 3 4 5 6 7 8 9 10
N= =Σx =Σy =Σ 2x =Σ 2y () =×Σ yx
(a) () =×Σ× yxN
(b) =Σ×Σ yx
(c) Subtract (b) from (a) () =Σ×Σ−×Σ× yxyxN
Appendix 1
(d) =Σ× 2xN
(e) Square the sum of x (Σx) and subtract this square from (d) ()[ ]=Σ−Σ× 22 xxN
(f) =Σ× 2yN
(g) Square the sum of y (Σy) and subtract this square from (f) ()[ ]=Σ−Σ× 2 yyN
(h) Multiply (e) and (g) ()[ ] ( )[ ]=Σ−Σ××Σ−Σ× 2222 yyNxxN
(i) Take the square root of (h) ()[] ()[ ]=Σ−Σ××Σ−Σ× 2222 yyNxxN
(j) Divide (c) by (i) () ()[] ()[] = Σ−Σ××Σ−Σ× Σ×Σ−×Σ×= 2222 yyNxxN yxyxN1
NOTE: The correlation coefficient (r) must not be less than 0.99.
c. Non-Linear Conversions. For non-linear parameter conversions, the following method, or method in (d) below, may be used to calculate the correlation coefficient. The Sum of Least Squares is used to determine the fit of data to a function in non-linear regression. The objective in the curve fit is to minimize the sum of the squared errors.
Coefficient of Determination or the Sum of Least Squares method is performed by using the following equation:
()( ) 2 ii n 1i xyRSS ∫−Σ= = where xi and yi are known values and f(xi) is the calculated y value from the curve fit function.
Appendix 1
d. Coefficient of Determination, R2 T E2 SS SS1R −= ( ) ( ) 2 iiiE 2 iiT yˆySS,yySS −Σ=−Σ= Where SSE is the RSS in paragraph (c) above.
SST is the Total Sum of Squares. The range of R2 is from 0 to 1.
0 = no correlation and the data is correlated when R2 = 1.
Appendix 2 APPENDIX 2. REVERSE DFDR DATA CORRELATION PROCEDURES
1. PURPOSE.
a. Reverse Engineer a DFDR Data Correlation Document. This appendix characterizes reverse DFDR data correlation procedures acceptable to the FAA. We outline steps you can take to reverse engineer a DFDR data correlation document. Reverse DFDR data correlation procedures can be useful if a baseline data correlation document does not exist for a particular aircraft installation. Instead of recreating a data correlation document, an aircraft operator may follow these procedures. This appendix may be beneficial in reducing time and cost to develop or obtain a data correlation document.
b. Ensuring Performance. The following procedure gives information to DFDR test engineers and operators who conduct maintenance checks and other DFDR airworthiness certification activities. These procedures may be used to ensure the DFDRS, as installed, is performing its intended function. Allowable tolerances in the CFRs are greater than those tolerances derived in this appendix. These procedures are an acceptable means to show compliance with DFDR operating requirements in parts 91, 121, 125, 129, and 135.
2. DEFINITIONS. Several key terms used in this appendix need to be identified and defined to establish an unambiguous understanding of the language. These terms defined herein are for purposes of this appendix material and are applicable to the following reverse DFDR data correlation procedures.
a. Conventional Form of Digital Outputs. When extracting the recorded DFDR data, the conventional form of digital outputs is the numerical format implementation of how the digital data is displayed. For example, data can be represented in the form of octal numbers, hexadecimals, etc. This digital output is commonly converted into decimal units, and further converted into useful engineering data.
b. Conversion Document. Information on how to represent a system’s EU in the form of decimal units or vice versa. Depending on the ARINC Specification 429 word structure, the conversion method may vary from classic analog look-up tables to digital binary representation high-order polynomial equations. A conversion document can be referred to as a DFDR’s “data map.”
c. DFDR Field Test. A validation check performed onboard an aircraft to compare actual data to recorded data. For the purposes of this definition, keep in mind that the data correlation document is unproducible. Other required validation steps must be performed and are described later in this appendix. The following steps are typical DFDR field test procedures.
(1) Test each required parameter over a precise and realistic functional range.
(2) Record the DFDR data output in any conventional form (i.e., hexadecimal, octal, binary, etc.).
(3) Using common mathematical techniques, convert the DFDR data output into decimal units, depending on the conventional form of digital output.
Appendix 2
(4) Plot each data output parameter in EU versus decimal units.
d. Input. A piece of information required to begin a procedure. During a procedure, inputs are intended to be used or manipulated to achieve a desired output.
e. Interface Control Documents (ICD).
(1) Data mapping documents that explain the wiring configuration of internal and external DFDRS component interfaces. All source system signals are sent to the recorder. These signals are traced internally to the final recording format. Every make, model, and series of aircraft has a related series of ICDs for recorded data. For example, a DFDAU ICD describes and defines the electrical interface characteristics and requirements of the line replaceable units (LRU) to the DFDAU.
(2) Data mapping documents contain expected signal input and output information for each recorded parameter type, which can be any of the following ARINC Specification 429 signal formats:
(a) Analog data bit,
(b) Discrete data bit,
(c) Coded discretes,
(d) Binary representation,
(e) Digital BCD, or
(f) Digital encoded parameter.
(3) Other information includes the parameter type, word, subframe, location of the bit(s) in the word (word structure), and total number of bits used in the word. This document may be used to obtain inputs for Procedure A (see paragraph 3).
f. Number of Bits. The number representing how much space is required to store the data in a digital word. This number can range from 1 to 12 per ARINC Characteristic 717. If a parameter resolution is not identified, then this number is critical to the useful effectiveness of this appendix. To determine the resolution by assessing the number of bits, see paragraph 2j.
g. Output. A piece of information obtained after the completion of a procedure. The outputs produced may be used as inputs for another procedure.
h. Parameter Detail Document (PDD). Digital parameter specific information. Like a DFDR ICD, this document may be used to obtain inputs for Procedure A.
i. Range. A set of functional and numerical values bounded by a maximum and a minimum. As defined by the input data to Procedure A, the functional range may not truly reflect the exact range of a particular aircraft operational or performance parameter. This appendix
Appendix 2 refers to range as the “change in range”, or by the symbol ΔR. For example, if given a range [] 21 R,R , then the total change in range is:
12 RRR −=Δ
j. Resolution. An EU representation of the least significant bit (LSB) in the word structure.
This LSB is important when calculating the value of a digital binary type parameter. If the parameter resolution is not identified in the input information, then the resolution must be determined. Given the number of bits and the range in EU, a linear resolution can be calculated by using the following equation:
Where, ΔR is the total change in range, derived in paragraph 2i, measured in EU, and NB is number of bits, the parameter resolution is denoted by:
() NB2 Rres Δ= NOTE: It is important to document an appropriate number of decimal places (or express the resolution as a fraction) to avoid the introduction and propagation of error.
3. REVERSE DFDR DATA CO RRELATION PROCEDURE A. This paragraph describes the first procedure that DFDR test engineers may follow in conjunction with Procedures B and C to develop an acceptable baseline correlation document, when no document exists.
a. Requirements. This paragraph identifies the required data items needed to begin reverse engineering the DFDR data correlation document.
(1) Procedure A requires a search for and an identification of parameter specific information. ICDs, PDDs, and conversion documents are resources that contain information to perform Procedure A. The required minimum inputs to conduct Procedure A are conversion algorithms (decimal units to EU), ranges (EU), and either resolutions or number of bits in the digital word.
(2) The following example illustrates how to find ΔR when given a parameter’s range. If the range of the roll attitude parameter is –180˚ to +180˚, then the total change in range, ΔR, is:
( ) °=°−−°+=Δ 360180180R The parameter resolution in EU may not be available from the resource documents. If the parameter resolution is not identified in the input information, then the resolution must be determined from the number of bits. If roll attitude is the parameter of interest, then the following is an example of how to solve for a linear resolution. Given the number of bits is 12 and the change in range is given in the previous example, the linear resolution can be solved by using the following equation:
Appendix 2 () 0879.0res 4096 360 2 Rres NB = =Δ=
(3) A conversion document contains the algorithms, tables, or codes to convert applicable parameters from EU to decimal units. This information is critical in completion of reverse data correlation. Depending upon the ARINC Specification 429 data word structure of a specific parameter, an algorithm or conversion equation, a look-up table, or a conversion code is required to perform the conversion. An example of a binary formatted data conversion algorithm is below.
In this example roll angle is measured in degrees, such that:
U.E.inanglerollthedenoteswhere 931399390.00465716 602082600.11550433249482610.00000035248068910.00000014 000031670.00000000000015150.00000000 unitDecimal 23 45 ϕ ϕϕϕ ϕϕ +×+×+× −×+×=
(4) Now that the required inputs for Procedure A are gathered, paragraph 3b lays out the foundation to derive baseline correlation data.
b. Process. This paragraph outlines the steps to create the baseline of manufacturer system-specific data.
(1) A baseline must be established that translates a 1 to 1 correlation between decimal units and EU for the full range of every parameter. For each parameter, use the conversion algorithm or other method to calculate the full range in decimal units.
(2) Begin plotting the lowest value in the full range against the respected decimal unit.
Then, increment the resolution to obtain decimal unit values for all NB2 range values. All NB2 values are plotted with an uncertainty of half the resolution, 2res± .
c. Data Application/Desired Output. This paragraph identifies the required data to be produced by following Procedure A.
(1) In Procedure A, DFDR parameter information was gathered to convert the full range from EU to decimal units. The conversion algorithm or other method was utilized to create a baseline of DFDR system data. The baseline conversion data must be stored or displayed in some documented fashion.
(2) If applicable, the parameter’s resolution must be converted from EU to decimal units.
In the case of a parameter with a non-linear resolution, an EU to decimal conversion must be considered from decimal count to decimal count. Section 5 discusses the significance and applicability of the parameter’s resolution to this appendix.
(3) A baseline plot for an identified parameter.
Appendix 2
(a) One example of displaying the baseline data is by plotting individual data points.
One implementation would be to plot decimal units as a function of EU, with increments of the resolution determined in paragraph 3c. The following linear baseline plot, Figure 2-1, is a continuation of the roll attitude example from previous paragraphs. Figure 2-2 shows an example of a nonlinear baseline plot.
(b) If a baseline plot cannot be established with reasonable accuracy, then ground station tools may be required to perform an accurate baseline plot of intermediate converted values. For example, some DFDRS implementations process synchro signals which increases both the complexity and accuracy of a decimal unit to EU conversion.
FIGURE 2-1. EXAMPLE LINEAR BASELINE PLOT OF EU TO DECIMAL UNITS Roll Attitude Parameter Conversion Data -180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180 -20 -16 -12 -8 -4 0 4 8 12 16 20 Decimal Units Engineering Units
Appendix 2 FIGURE 2-2. EXAMPLE NON-LINEAR BASELINE PLOT OF EU TO DECIMAL UNITS Electric Coarse Altitude Parameter Conversion Data -10000 0 10000 20000 30000 40000 50000 -200 0 200 400 600 800 1000 1200 1400 1600 Decimal Units Engineering Units
(4) Once data storage or display is complete, this information is used in paragraph 5 as a baseline to determine compliance with the CFR.
4. REVERSE DFDR DATA CO RRELATION PROCEDURE B. This paragraph identifies the data items needed to complete the required aircraft test of DFDR data reverse correlation.
Accomplishing this procedure depends on the availability of the aircraft to be tested.
a. Requirements. Procedure B requires the data ranges for each parameter, a DFDRS-equipped aircraft, and all equipment necessary to test the onboard DFDRS. The decimal unit to EU conversion algorithm or method is required. The operator or test engineer must have a predetermined list of data points to test for each parameter through the static and full dynamic ranges. This list of data points must be in EU and correlate to one of the 2NB data points obtained in Procedure A. It is also useful to have a tool capable of converting conventional forms of digital outputs into decimal units.
NOTE: There are cases where certain types of parameters cannot be tested in the airplane environment. These parameters can only be stimulated in a lab environment and applied to the airplane through analysis. For example, a computer failure can be simulated in the lab environment and the software paths of the acquisition unit can be confirmed. This testing can be applied to the airplane where it is rare that one can force working equipment to fail for test purposes. Credit should be given that source systems that provide data to the acquisition unit had these functions tested during their certification.