Appendix 1
b. Frames and Subframes. Specifically, they generate 12-bit words with a word rate that may vary, i.e., 32, 64, 128, 256, 512, or 1024 (words/second). The data is organized into frames that are repeated every 4 seconds. Each frame consists of 4 subframes. Each subframe occupies 1 second in the data stream, however, not all data streams are ARINC compliant and a subframe may occupy more or less than 1 second. The first word in each subframe normally provides the frame synchronization pattern. The data stream format should enable the analyst to locate header information and parameter information in the DFDR output.
c. Header Information. For DFDRs that conform to ARINC characteristics, the following information should be stored in a header file. (For other DFDR frame structures, the number of subframes per frame must be omitted and the frame structure must be uniquely described.) The header file must include:
(1) Aircraft make and model.
(2) Aircraft serial number.
(3) DFDR make and model/part number.
(4) Number of subframes per frame, for a fixed-frame. Or a description of each of the frame formats in a multiple-frame format data stream.
d. Record Information.
(1) For a fixed-frame format:
(a) Bits in the DFDR word.
(b) Number of DFDR words in a subframe.
(c) Time duration of the subframe (seconds).
(2) For a multiple-frame format:
(a) List of parameters in the frame, in order.
(b) The number of bits used to store each parameter.
e. Parameter Information. The identification for each parameter should include:
(1) Parameter name—must be unique from all other parameters recorded.
(2) Mnemonic code—a common abbreviation for the parameter, which must be unique from the mnemonic codes of all other parameters recorded.
f. Parameter Location. Both component(s) and timing information should be provided for each parameter sample. Usually there is only one component. For samples having more than one component the components should be ordered from least significant to most significant in the
Appendix 1 data stream. Each sample location for a parameter should have the same total number of bits. The following items must be provided for a parameter sample location:
(1) Subframe number.
(2) Word number.
(3) Bit numbers.
(4) If superframe cycles are used, also provide:
(a) Cycle counter name.
(b) Cycle numbers.
5. LEXICON OF MNEMONIC CODES. If mnemonic codes are used, a lexicon of these codes must be provided.
6. EU CONVERSION. EU conversions must convert decimal counts to the parameter value measured. Where the parameter is used by the pilot in flight (e.g., airspeed, altitude, and heading), the conversion must be correlated to the value shown to the pilot. Other values must be correlated to values sensed by the aircraft. Where an EU conversion results in an interim parameter (e.g., alternating current voltage ratio No. 1, frequency, direct current voltage ratio No. 2, potentiometer, or synchro angle) the conversion formula that converts this interim parameter to the actual parameter must also be provided. Each recorded parameter must be converted to an EU. Both signage (whether or not the raw data contains a plus or minus sign and the location of the sign in the parameter bits) and raw data range must be provided. Standardized signage is provided in ARINC Specification 647A appendices E and F. Instructions must be provided to enable the accident investigator to convert the recorded data to EU An example of acceptable conversion equations are as follows:
a. Linear Equation.
1010 CNTSAAEU ×+= where: EU is the value in engineering units 0CNTSthewhenEUofnumbertheisA 100 = 1A is the slope of the line in EU per decimal count 10CNTS is the number of binary or binary coded decimal (BCD) counts converted to decimal counts
Appendix 1
b. Piece-wise Linear Equation. In some instances it may be necessary to correlate the data using multiple linear equations. For example, the data of Figure 1-1 was obtained using two linear equations as follows:
For Altitude (EU) feet500≤ For Altitude (EU) feet500> ()() 0200231.0A 002.0A10 = −= ( )() 013351.0A 29673.0A10 = −= where, ≤ indicates equal to or less than > indicates greater than
c. Polynomial Equation.
X2 10x1021010 CNTSACNTSACNTSAAEU ×+×+×+= K where, EU is the value in engineering units 10CNTS is the number of binary or BCD counts converted to decimal counts 0A is the number of EU when the 0CNTS10 = X21 A,A,A K are coefficients developed by a curve fit
d. Unique Equation. Where a unique equation applies, explicit documentation must be developed at the time of certification and approved by the FAA. This documentation may contain sufficient information to allow a tool programmer the ability to develop a conversion that uses his tool efficiently.
7. EU DATA CORRELATION. When certifying new parameter implementations, an acceptable procedure to correlate the recorded data to the data derived from the conversion equation follows:
(1) Set or read the device being measured (radio altimeter altitude for example) to a known fixed data point.
(2) Record the data in the Raw Data (EU) column of Table 1-2.
(3) Record the decimal counts from the DFDR record in the 10CNTS column of Table 1-2.
NOTE: The DFDR normally records counts in a binary format. Most equipment manufacturers provide a digital output port and test equipment to access the data. Data can be displayed in binary, octal, or hexadecimal format with octal being the most common. Convert the counts to decimals using instructions provided by the equipment manufacturer.
(4) Repeat steps (1) through (3) above until a sufficient number of data points have been collected for correlation.
Appendix 1 NOTE: The number of required data points will vary depending upon the parameter and the transducer. As a minimum, three data points must be recorded for linear equation parameters, one at the mid-point (or null point) and the others at each end point of the range for the parameter. For polynomial equation parameters, the more data points taken for correlation will produce a higher quality conversion formula. Also, the recorded data points must include one at each end of the range and sufficient intermediate points to produce an accurate conversion formula. For piece-wise linear equations, a minimum of three data points must be recorded for each linear segment of the equation.
(5) Derive the EU value for each recorded 10CNTS value using the conversion equation or method provided. Record the derived value for each data point. When necessary intermediate conversion methods may be used to improve conversion accuracy of the parameter.
(6) The tabulated raw data and the derived data must also be plotted to confirm the prediction capability of the equation (linear, piece-wise linear, polynomial or unique). The plot must cover the full operating range for the parameter. See Figure 1-1 for an example plot. In the example of Figure 1-1, the data is so closely correlated (correlation coefficient = 0.99985) that the raw data and the derived data appear to be superimposed on each other.
FIGURE 1-1. AN EXAMPLE PLOT OF THE RADIO ALTIMETER IN FEET VERSUS
DECIMAL COUNTS
8. DISCRETE DECIPHER LOGIC. The correlation documentation must contain decipher logic for discrete parameters. The decipher logic must identify the status of the discrete represented by each binary state (e.g., “0” =OFF, “1”=ON). In instances where a group of discrete states is represented by multiple binary bits, the entire discrete word must be presented in the correlation document. See Table 1-1. The word slot, subframe, and bit logic for the specific discrete codes must be identified in the documentation.
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